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The word research itself is a combination of “ re ” and “ search ,” which is meant by a systematic investigation to gain new knowledge from already existing facts. Frankly speaking, research may be defined as a scientific understanding of existing knowledge and deriving new knowledge to be applied for the betterment of the mankind. In the words of Wernher von Braun (a German philosopher), “ Research is what I’m doing when I don’t know what I’m doing .” It is basically the search for truth/facts. The significant contribution of research deals with the progress of the nation as well as an individual with commercial, social, and educational advantages. Albert Szent Gyorgyi (Hungarian Biochemist, Nobel Prize 1937) writes “ Research is to see what everybody else has seen and think what nobody has thought .” Research may be an important parameter to judge the development of any nation/generation. According to Clifford Woody (American philosopher, 1939), “ Research comprises of defining and redefining problems, formulating the hypothesis for suggested solutions, collecting, organizing and evaluating data, making deductions and reaching conclusion and further testing the conclusion whether they fit into formulating the hypothesis .” The major objectives of research are to find out a hidden and undiscovered truth of the nature/society. There are various objectives behind undertaking research by individuals as well as various organizations/universities. Some philosophical objectives behind any research include:
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Bairagi V, Munot MV (2019) Research methodology. A practical and scientific approach. CRC Press Taylor & Francis Group, New York, NY
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Pruzan P (2016) Research methodology: the aims, practices and ethics of science. Springer International Publishing Switzerland, Cham
Smeyers P, Depaepe M (2018) Educational research: ethics, social justice, and funding dynamics. Springer International Publishing AG, (part of Springer Nature), Cham
Yadav SK (2015) Elements of research writing. UDH Publishers and Distributers, New Delhi
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Shri Jagdishprasad Jhabarmal Tibrewala University, Jhunjhunu, Rajasthan, India
Santosh Kumar Yadav
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Correspondence to Santosh Kumar Yadav .
Explain the term “research” in view of two philosophers.
Briefly describe the different steps involved in a research process.
Describe the different types of research, clearly pointing out the difference between an experiment and a survey.
“Empirical research in India in particular creates so many problems for the researchers.” State the problems that are usually faced by such researchers.
“Creative management, whether in public administration or private industry, depends on methods of inquiry that maintain objectivity, clarity, accuracy, and consistency.” Discuss this statement and examine the significance of research.
What is research problem? Define the main issues which should receive the attention of the researcher in formulating the research problem. Give suitable examples to elucidate your points.
“Knowing what data are available often serves to narrow down the problem itself as well as the technique that might be used.” Explain the underlying idea in this statement in the context of defining a research problem.
What is research design? Discuss the basis of stratification to be employed in sampling public opinion on inflation.
Give your understanding of a good research design. Is single research design suitable in all research studies? If not, why?
“It is never safe to take published statistics at their face value without knowing their meaning and limitations.” Elucidate this statement by enumerating and explaining the various points which you would consider before using any published data. Illustrate your answer by examples wherever possible.
“Experimental method of research is not suitable in management field.” Discuss, what are the problems in the introduction of this research design in business organization?
What are common features of good research?
How many ways the philosophical scientific knowledge may be classified in the research?
Explain Wilfred Carr’s concept of educational philosophy and theory.
What is the difference between philosophy of research and philosophy in research?
What is the physical relationship between learning and experience?
What is the impact of action research on the scholar’s learning?
What are philosophical features of a good research study?
Explain the role of a philosopher in an interdisciplinary research.
Write Short Notes on the following:
Educational Research and Philosophy
Philosopher in the Classroom
Educational Research: Pursuit of Truth
Interdisciplinary Research
Pragmatic Theory of Knowledge
Ethical Codes and Academic Independence
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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
Yadav, S.K. (2023). Philosophy of Research: An Introduction. In: Research and Publication Ethics. Springer, Cham. https://doi.org/10.1007/978-3-031-26971-4_1
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What is a hypothesis.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Attrition refers to participants leaving a study. It always happens to some extent—for example, in randomized controlled trials for medical research.
Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group . As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased .
Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.
Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.
Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.
A cycle of inquiry is another name for action research . It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”
To make quantitative observations , you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.
Criterion validity and construct validity are both types of measurement validity . In other words, they both show you how accurately a method measures something.
While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.
Construct validity is often considered the overarching type of measurement validity . You need to have face validity , content validity , and criterion validity in order to achieve construct validity.
Convergent validity and discriminant validity are both subtypes of construct validity . Together, they help you evaluate whether a test measures the concept it was designed to measure.
You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.
Content validity shows you how accurately a test or other measurement method taps into the various aspects of the specific construct you are researching.
In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.
The higher the content validity, the more accurate the measurement of the construct.
If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.
Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.
When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.
For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).
On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analyzing whether each one covers the aspects that the test was designed to cover.
A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.
Snowball sampling is a non-probability sampling method . Unlike probability sampling (which involves some form of random selection ), the initial individuals selected to be studied are the ones who recruit new participants.
Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.
Snowball sampling is a non-probability sampling method , where there is not an equal chance for every member of the population to be included in the sample .
This means that you cannot use inferential statistics and make generalizations —often the goal of quantitative research . As such, a snowball sample is not representative of the target population and is usually a better fit for qualitative research .
Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones.
Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias .
Snowball sampling is best used in the following cases:
The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.
Reproducibility and replicability are related terms.
Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.
The main difference is that in stratified sampling, you draw a random sample from each subgroup ( probability sampling ). In quota sampling you select a predetermined number or proportion of units, in a non-random manner ( non-probability sampling ).
Purposive and convenience sampling are both sampling methods that are typically used in qualitative data collection.
A convenience sample is drawn from a source that is conveniently accessible to the researcher. Convenience sampling does not distinguish characteristics among the participants. On the other hand, purposive sampling focuses on selecting participants possessing characteristics associated with the research study.
The findings of studies based on either convenience or purposive sampling can only be generalized to the (sub)population from which the sample is drawn, and not to the entire population.
Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.
On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.
Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.
However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.
In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection, using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.
A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.
Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.
Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .
A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.
The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .
An observational study is a great choice for you if your research question is based purely on observations. If there are ethical, logistical, or practical concerns that prevent you from conducting a traditional experiment , an observational study may be a good choice. In an observational study, there is no interference or manipulation of the research subjects, as well as no control or treatment groups .
It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.
While experts have a deep understanding of research methods , the people you’re studying can provide you with valuable insights you may have missed otherwise.
Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.
Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.
Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.
Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.
You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity .
When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.
Construct validity is often considered the overarching type of measurement validity , because it covers all of the other types. You need to have face validity , content validity , and criterion validity to achieve construct validity.
Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity , which includes construct validity, face validity , and criterion validity.
There are two subtypes of construct validity.
Naturalistic observation is a valuable tool because of its flexibility, external validity , and suitability for topics that can’t be studied in a lab setting.
The downsides of naturalistic observation include its lack of scientific control , ethical considerations , and potential for bias from observers and subjects.
Naturalistic observation is a qualitative research method where you record the behaviors of your research subjects in real world settings. You avoid interfering or influencing anything in a naturalistic observation.
You can think of naturalistic observation as “people watching” with a purpose.
A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.
In statistics, dependent variables are also called:
An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.
Independent variables are also called:
As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups. Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions , which can bias your responses.
Overall, your focus group questions should be:
A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when:
More flexible interview options include semi-structured interviews , unstructured interviews , and focus groups .
Social desirability bias is the tendency for interview participants to give responses that will be viewed favorably by the interviewer or other participants. It occurs in all types of interviews and surveys , but is most common in semi-structured interviews , unstructured interviews , and focus groups .
Social desirability bias can be mitigated by ensuring participants feel at ease and comfortable sharing their views. Make sure to pay attention to your own body language and any physical or verbal cues, such as nodding or widening your eyes.
This type of bias can also occur in observations if the participants know they’re being observed. They might alter their behavior accordingly.
The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.
There is a risk of an interviewer effect in all types of interviews , but it can be mitigated by writing really high-quality interview questions.
A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:
An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.
Unstructured interviews are best used when:
The four most common types of interviews are:
Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research .
In research, you might have come across something called the hypothetico-deductive method . It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.
Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.
Deductive reasoning is also called deductive logic.
There are many different types of inductive reasoning that people use formally or informally.
Here are a few common types:
Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.
Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.
In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.
Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.
Inductive reasoning is also called inductive logic or bottom-up reasoning.
Triangulation can help:
But triangulation can also pose problems:
There are four main types of triangulation :
Many academic fields use peer review , largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.
However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure.
Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.
Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field. It acts as a first defense, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.
Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.
In general, the peer review process follows the following steps:
Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.
You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.
Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.
Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.
Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.
Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.
Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.
Dirty data can come from any part of the research process, including poor research design , inappropriate measurement materials, or flawed data entry.
Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.
For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.
After data collection, you can use data standardization and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.
Every dataset requires different techniques to clean dirty data , but you need to address these issues in a systematic way. You focus on finding and resolving data points that don’t agree or fit with the rest of your dataset.
These data might be missing values, outliers, duplicate values, incorrectly formatted, or irrelevant. You’ll start with screening and diagnosing your data. Then, you’ll often standardize and accept or remove data to make your dataset consistent and valid.
Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors , but cleaning your data helps you minimize or resolve these.
Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.
Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.
In this process, you review, analyze, detect, modify, or remove “dirty” data to make your dataset “clean.” Data cleaning is also called data cleansing or data scrubbing.
Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.
These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.
Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations .
You can only guarantee anonymity by not collecting any personally identifying information—for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.
You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.
Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.
Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.
Scientists and researchers must always adhere to a certain code of conduct when collecting data from others .
These considerations protect the rights of research participants, enhance research validity , and maintain scientific integrity.
In multistage sampling , you can use probability or non-probability sampling methods .
For a probability sample, you have to conduct probability sampling at every stage.
You can mix it up by using simple random sampling , systematic sampling , or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.
Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.
But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples .
These are four of the most common mixed methods designs :
Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.
Triangulation is mainly used in qualitative research , but it’s also commonly applied in quantitative research . Mixed methods research always uses triangulation.
In multistage sampling , or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.
This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from state to city to neighborhood) to create a sample that’s less expensive and time-consuming to collect data from.
No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.
To find the slope of the line, you’ll need to perform a regression analysis .
Correlation coefficients always range between -1 and 1.
The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.
The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.
These are the assumptions your data must meet if you want to use Pearson’s r :
Quantitative research designs can be divided into two main categories:
Qualitative research designs tend to be more flexible. Common types of qualitative design include case study , ethnography , and grounded theory designs.
A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources . This allows you to draw valid , trustworthy conclusions.
The priorities of a research design can vary depending on the field, but you usually have to specify:
A research design is a strategy for answering your research question . It defines your overall approach and determines how you will collect and analyze data.
Questionnaires can be self-administered or researcher-administered.
Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or through mail. All questions are standardized so that all respondents receive the same questions with identical wording.
Researcher-administered questionnaires are interviews that take place by phone, in-person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.
You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomization can minimize the bias from order effects.
Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.
Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.
A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.
The third variable and directionality problems are two main reasons why correlation isn’t causation .
The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.
The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.
Correlation describes an association between variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.
Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.
While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy .
Controlled experiments establish causality, whereas correlational studies only show associations between variables.
In general, correlational research is high in external validity while experimental research is high in internal validity .
A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.
A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.
Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.
A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .
A correlation reflects the strength and/or direction of the association between two or more variables.
Random error is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables .
You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking (blinding) where possible.
Systematic error is generally a bigger problem in research.
With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample , the errors in different directions will cancel each other out.
Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions ( Type I and II errors ) about the relationship between the variables you’re studying.
Random and systematic error are two types of measurement error.
Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).
Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).
On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.
The term “ explanatory variable ” is sometimes preferred over “ independent variable ” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.
Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.
The difference between explanatory and response variables is simple:
In a controlled experiment , all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:
Depending on your study topic, there are various other methods of controlling variables .
There are 4 main types of extraneous variables :
An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.
A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.
In a factorial design, multiple independent variables are tested.
If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.
Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful .
Advantages:
Disadvantages:
While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design .
Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.
In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.
In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.
The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.
Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.
In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.
To implement random assignment , assign a unique number to every member of your study’s sample .
Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.
Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.
In contrast, random assignment is a way of sorting the sample into control and experimental groups.
Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.
In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.
“Controlling for a variable” means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.
Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs . That way, you can isolate the control variable’s effects from the relationship between the variables of interest.
Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity .
If you don’t control relevant extraneous variables , they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable .
A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.
Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.
Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.
If something is a mediating variable :
A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.
A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.
There are three key steps in systematic sampling :
Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .
Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.
For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.
You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.
Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.
For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.
In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).
Once divided, each subgroup is randomly sampled using another probability sampling method.
Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area.
However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole.
There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.
Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.
The clusters should ideally each be mini-representations of the population as a whole.
If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,
If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.
The American Community Survey is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.
Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.
Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .
Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity as they can use real-world interventions instead of artificial laboratory settings.
A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.
Blinding is important to reduce research bias (e.g., observer bias , demand characteristics ) and ensure a study’s internal validity .
If participants know whether they are in a control or treatment group , they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.
Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment .
A true experiment (a.k.a. a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.
However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).
For strong internal validity , it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.
An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.
Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.
Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.
The type of data determines what statistical tests you should use to analyze your data.
A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.
To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.
In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).
The process of turning abstract concepts into measurable variables and indicators is called operationalization .
There are various approaches to qualitative data analysis , but they all share five steps in common:
The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .
There are five common approaches to qualitative research :
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
Operationalization means turning abstract conceptual ideas into measurable observations.
For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.
Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.
When conducting research, collecting original data has significant advantages:
However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.
Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.
There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.
In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables.
In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable .
In statistical control , you include potential confounders as variables in your regression .
In randomization , you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.
A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.
Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.
To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.
Yes, but including more than one of either type requires multiple research questions .
For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.
You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .
To ensure the internal validity of an experiment , you should only change one independent variable at a time.
No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!
You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .
Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.
In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.
Common non-probability sampling methods include convenience sampling , voluntary response sampling, purposive sampling , snowball sampling, and quota sampling .
Probability sampling means that every member of the target population has a known chance of being included in the sample.
Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .
Using careful research design and sampling procedures can help you avoid sampling bias . Oversampling can be used to correct undercoverage bias .
Some common types of sampling bias include self-selection bias , nonresponse bias , undercoverage bias , survivorship bias , pre-screening or advertising bias, and healthy user bias.
Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.
A sampling error is the difference between a population parameter and a sample statistic .
A statistic refers to measures about the sample , while a parameter refers to measures about the population .
Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.
Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.
There are seven threats to external validity : selection bias , history, experimenter effect, Hawthorne effect , testing effect, aptitude-treatment and situation effect.
The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).
The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.
Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study .
Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.
Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.
Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.
The 1970 British Cohort Study , which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study .
Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.
Longitudinal studies and cross-sectional studies are two different types of research design . In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.
Longitudinal study | Cross-sectional study |
---|---|
observations | Observations at a in time |
Observes the multiple times | Observes (a “cross-section”) in the population |
Follows in participants over time | Provides of society at a given point |
There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias , regression to the mean, social interaction and attrition .
Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.
In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .
The research methods you use depend on the type of data you need to answer your research question .
A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.
A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.
In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.
Discrete and continuous variables are two types of quantitative variables :
Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).
Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).
You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .
You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .
In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:
Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .
Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:
When designing the experiment, you decide:
Experimental design is essential to the internal and external validity of your experiment.
I nternal validity is the degree of confidence that the causal relationship you are testing is not influenced by other factors or variables .
External validity is the extent to which your results can be generalized to other contexts.
The validity of your experiment depends on your experimental design .
Reliability and validity are both about how well a method measures something:
If you are doing experimental research, you also have to consider the internal and external validity of your experiment.
A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.
In statistics, sampling allows you to test a hypothesis about the characteristics of a population.
Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.
Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.
Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.
Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).
In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .
In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.
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What it is and how it's used in sociology
A hypothesis is a prediction of what will be found at the outcome of a research project and is typically focused on the relationship between two different variables studied in the research. It is usually based on both theoretical expectations about how things work and already existing scientific evidence.
Within social science, a hypothesis can take two forms. It can predict that there is no relationship between two variables, in which case it is a null hypothesis . Or, it can predict the existence of a relationship between variables, which is known as an alternative hypothesis.
In either case, the variable that is thought to either affect or not affect the outcome is known as the independent variable, and the variable that is thought to either be affected or not is the dependent variable.
Researchers seek to determine whether or not their hypothesis, or hypotheses if they have more than one, will prove true. Sometimes they do, and sometimes they do not. Either way, the research is considered successful if one can conclude whether or not a hypothesis is true.
A researcher has a null hypothesis when she or he believes, based on theory and existing scientific evidence, that there will not be a relationship between two variables. For example, when examining what factors influence a person's highest level of education within the U.S., a researcher might expect that place of birth, number of siblings, and religion would not have an impact on the level of education. This would mean the researcher has stated three null hypotheses.
Taking the same example, a researcher might expect that the economic class and educational attainment of one's parents, and the race of the person in question are likely to have an effect on one's educational attainment. Existing evidence and social theories that recognize the connections between wealth and cultural resources , and how race affects access to rights and resources in the U.S. , would suggest that both economic class and educational attainment of the one's parents would have a positive effect on educational attainment. In this case, economic class and educational attainment of one's parents are independent variables, and one's educational attainment is the dependent variable—it is hypothesized to be dependent on the other two.
Conversely, an informed researcher would expect that being a race other than white in the U.S. is likely to have a negative impact on a person's educational attainment. This would be characterized as a negative relationship, wherein being a person of color has a negative effect on one's educational attainment. In reality, this hypothesis proves true, with the exception of Asian Americans , who go to college at a higher rate than whites do. However, Blacks and Hispanics and Latinos are far less likely than whites and Asian Americans to go to college.
Formulating a hypothesis can take place at the very beginning of a research project , or after a bit of research has already been done. Sometimes a researcher knows right from the start which variables she is interested in studying, and she may already have a hunch about their relationships. Other times, a researcher may have an interest in a particular topic, trend, or phenomenon, but he may not know enough about it to identify variables or formulate a hypothesis.
Whenever a hypothesis is formulated, the most important thing is to be precise about what one's variables are, what the nature of the relationship between them might be, and how one can go about conducting a study of them.
Updated by Nicki Lisa Cole, Ph.D
On the scope of scientific hypotheses.
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Did you know.
The Difference Between Hypothesis and Theory
A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.
A hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested.
A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, it is understood to be more likely to be true than a hypothesis is.
In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.
Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.
The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)
This mistake is one of projection: since we use theory in general to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.
The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”
While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."
hypothesis , theory , law mean a formula derived by inference from scientific data that explains a principle operating in nature.
hypothesis implies insufficient evidence to provide more than a tentative explanation.
theory implies a greater range of evidence and greater likelihood of truth.
law implies a statement of order and relation in nature that has been found to be invariable under the same conditions.
These examples are programmatically compiled from various online sources to illustrate current usage of the word 'hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.
Greek, from hypotithenai to put under, suppose, from hypo- + tithenai to put — more at do
1641, in the meaning defined at sense 1a
This is the Difference Between a...
In scientific reasoning, they're two completely different things
hypothermia
hypothesize
“Hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/hypothesis. Accessed 29 Aug. 2024.
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Your partner for better health, hypothesis in research: definition, types and importance .
April 21, 2020 Kusum Wagle Epidemiology 0
Table of Contents
1. Simple Hypothesis:
2. Complex Hypothesis:
3. Working or Research Hypothesis:
4. Null Hypothesis:
5. Alternative Hypothesis:
6. Logical Hypothesis:
7. Statistical Hypothesis:
Although there are different types of hypothesis, the most commonly and used hypothesis are Null hypothesis and alternate hypothesis . So, what is the difference between null hypothesis and alternate hypothesis? Let’s have a look:
A null hypothesis represents the hypothesis that there is | An alternative hypothesis is the opposite of the null hypothesis where |
In case of null hypothesis, researcher tries to invalidate or reject the hypothesis.
| In an alternative hypothesis, the researcher wants to show or prove some relationship between variables. |
It is an assumption that specifies a possible truth to an event where there is | It is an assumption that describes an alternative truth where there is or some difference. |
Null hypothesis is a statement that , no effect and no any differences between variables. | Alternative hypothesis is a statement that between variables. |
If null hypothesis is true, any discrepancy between observed data and the hypothesis is only due to chance. | If alternative hypothesis is true, the observed discrepancy between the observed data and the null hypothesis is not due to chance. |
A null hypothesis is denoted as H . | An alternative hypothesis is denoted as H or H . |
There is no association between use of oral contraceptive and blood cancer H : µ = 0 | There is no association between use of oral contraceptive and blood cancer H : µ ≠ 0 |
https://ocw.jhsph.edu/courses/StatisticalReasoning1/PDFs/2009/BiostatisticsLecture4.pdf
https://keydifferences.com/difference-between-type-i-and-type-ii-errors.html
https://www.khanacademy.org/math/ap-statistics/tests-significance-ap/error-probabilities-power/a/consequences-errors-significance
https://stattrek.com/hypothesis-test/hypothesis-testing.aspx
http://davidmlane.com/hyperstat/A2917.html
https://study.com/academy/lesson/what-is-a-hypothesis-definition-lesson-quiz.html
https://keydifferences.com/difference-between-null-and-alternative-hypothesis.html
https://blog.minitab.com/blog/adventures-in-statistics-2/understanding-hypothesis-tests-why-we-need-to-use-hypothesis-tests-in-statistics
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General Education
Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.
But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including:
So let’s get started!
Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid.
As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.
Hypotheses are one part of what’s called the scientific method . Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):
You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!
After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.
There are two types of variables: independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable.
Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets.
Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.
The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.
As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.
Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.
Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.
When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.
The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement!
In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.
Additionally, keep in mind that hypotheses can range from very specific to very broad. These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.
Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.
First of all, if-then hypotheses typically follow this formula:
If ____ happens, then ____ will happen.
The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life:
In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades).
You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:
“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”
It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.
Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .
One null hypothesis for the cell phone and sleep study from the last section might say:
“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.”
In this case, this is a null hypothesis because it’s asking the opposite of the original thesis!
Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:
“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”
In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:
“If people have many followers on Instagram, they will spend more time on the app than people who have less.”
You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship.
If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.
At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think.
Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.
Improbable hypotheses generally go against science, as well. Take this hypothesis example:
“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.”
This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.
The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.
Here’s what we mean. Which of the following sentences makes more sense to the common person?
If the kerning is greater than average, more words will be read per minute.
If the space between letters is greater than average, more words will be read per minute.
For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible.
Good hypotheses ensure that you can observe the results.
In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.
Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable.
In writing your hypothesis, always keep in mind how you'll execute the experiment.
Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.
Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?
We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.
You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?
You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:
If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”
Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”
These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.
To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come and how many leave. You also write down the temperature on the hour.
After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.
Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?
Here’s what your hypotheses might look like:
If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”
Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”
This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).
While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment.
However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this:
If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”
Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”
Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.
You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while:
If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.
Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.
You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?
This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again!
The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.
Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.
If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)
If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.
If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home
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1 Laboratory of Gene Technology, Department of Biosystems, KU Leuven, Leuven Belgium
Scientific research progresses by the dialectic dialogue between hypothesis building and the experimental testing of these hypotheses. Microbiologists as biologists in general can rely on an increasing set of sophisticated experimental methods for hypothesis testing such that many scientists maintain that progress in biology essentially comes with new experimental tools. While this is certainly true, the importance of hypothesis building in science should not be neglected. Some scientists rely on intuition for hypothesis building. However, there is also a large body of philosophical thinking on hypothesis building whose knowledge may be of use to young scientists. The present essay presents a primer into philosophical thoughts on hypothesis building and illustrates it with two hypotheses that played a major role in the history of science (the parallel axiom and the fifth element hypothesis). It continues with philosophical concepts on hypotheses as a calculus that fits observations (Copernicus), the need for plausibility (Descartes and Gilbert) and for explicatory power imposing a strong selection on theories (Darwin, James and Dewey). Galilei introduced and James and Poincaré later justified the reductionist principle in hypothesis building. Waddington stressed the feed‐forward aspect of fruitful hypothesis building, while Poincaré called for a dialogue between experiment and hypothesis and distinguished false, true, fruitful and dangerous hypotheses. Theoretical biology plays a much lesser role than theoretical physics because physical thinking strives for unification principle across the universe while biology is confronted with a breathtaking diversity of life forms and its historical development on a single planet. Knowledge of the philosophical foundations on hypothesis building in science might stimulate more hypothesis‐driven experimentation that simple observation‐oriented “fishing expeditions” in biological research.
Scientific research progresses by the dialectic dialogue between hypothesis building and the experimental testing of these hypotheses. Microbiologists can rely on an increasing set of sophisticated experimental methods for hypothesis testing but the importance of hypothesis building in science should not be neglected. This Lilliput offers a primer on philosophical concepts on hypotheses in science.
Philosophy of science and the theory of knowledge (epistemology) are important branches of philosophy. However, philosophy has over the centuries lost its dominant role it enjoyed in antiquity and became in Medieval Ages the maid of theology (ancilla theologiae) and after the rise of natural sciences and its technological applications many practising scientists and the general public doubt whether they need philosophical concepts in their professional and private life. This is in the opinion of the writer of this article, an applied microbiologist, shortsighted for several reasons. Philosophers of the 20th century have made important contributions to the theory of knowledge, and many eminent scientists grew interested in philosophical problems. Mathematics which plays such a prominent role in physics and increasingly also in other branches of science is a hybrid: to some extent, it is the paradigm of an exact science while its abstract aspects are deeply rooted in philosophical thinking. In the present essay, the focus is on hypothesis and hypothesis building in science, essentially it is a compilation what philosophers and scientists thought about this subject in past and present. The controversy between the mathematical mind and that of the practical mind is an old one. The philosopher, physicist and mathematician Pascal ( 1623 –1662a) wrote in his Pensées : “Mathematicians who are only mathematicians have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate. They are only right when the principles are quite clear. And men of intuition cannot have the patience to reach to first principles of things speculative and conceptional, which they have never seen in the world and which are altogether out of the common. The intellect can be strong and narrow, and can be comprehensive and weak.” Hypothesis building is an act both of intuition and exact thinking and I hope that theoretical knowledge about hypothesis building will also profit young microbiologists.
In the following, I will illustrate the importance of hypothesis building for the history of science and the development of knowledge and illustrate it with two famous concepts, the parallel axiom in mathematics and the five elements hypothesis in physics.
The prominent role of hypotheses in the development of science becomes already clear in the first science book of the Western civilization: Euclid's The Elements written about 300 BC starts with a set of statements called Definitions, Postulates and Common Notions that lay out the foundation of geometry (Euclid, c.323‐c.283 ). This axiomatic approach is very modern as exemplified by the fact that Euclid's book remained for long time after the Bible the most read book in the Western hemisphere and a backbone of school teaching in mathematics. Euclid's twenty‐three definitions start with sentences such as “1. A point is that which has no part; 2. A line is breadthless length; 3. The extremities of a line are points”; and continues with the definition of angles (“8. A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line”) and that of circles, triangles and quadrilateral figures. For the history of science, the 23rd definition of parallels is particularly interesting: “Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction”. This is the famous parallel axiom. It is clear that the parallel axiom cannot be the result of experimental observations, but must be a concept created in the mind. Euclid ends with five Common Notions (“1. Things which are equal to the same thing are also equal to one another, to 5. The whole is greater than the part”). The establishment of a contradiction‐free system for a branch of mathematics based on a set of axioms from which theorems were deduced was revolutionary modern. Hilbert ( 1899 ) formulated a sound modern formulation for Euclidian geometry. Hilbert's axiom system contains the notions “point, line and plane” and the concepts of “betweenness, containment and congruence” leading to five axioms, namely the axioms of Incidence (“Verknüpfung”), of Order (“Anordnung”), of Congruence, of Continuity (“Stetigkeit”) and of Parallels.
Philosophers gave various explanations for the origin of the Euclidean hypotheses or axioms. Plato considered geometrical figures as related to ideas (the true things behind the world of appearances). Aristoteles considered geometric figures as abstractions of physical bodies. Descartes perceived geometric figures as inborn ideas from extended bodies ( res extensa ), while Pascal thought that the axioms of Euclidian geometry were derived from intuition. Kant reasoned that Euclidian geometry represented a priori perceptions of space. Newton considered geometry as part of general mechanics linked to theories of measurement. Hilbert argued that the axioms of mathematical geometry are neither the result of contemplation (“Anschauung”) nor of psychological source. For him, axioms were formal propositions (“formale Aussageformen”) characterized by consistency (“Widerspruchsfreiheit”, i.e. absence of contradiction) (Mittelstrass, 1980a ).
Axioms were also differently defined by philosophers. In Topics , Aristoteles calls axioms the assumptions taken up by one partner of a dialogue to initiate a dialectic discussion. Plato states that an axiom needs to be an acceptable or credible proposition, which cannot be justified by reference to other statements. Yet, a justification is not necessary because an axiom is an evident statement. In modern definition, axioms are methodical first sentences in the foundation of a deductive science (Mittelstrass, 1980a ). In Posterior Analytics , Aristotle defines postulates as positions which are at least initially not accepted by the dialogue partners while hypotheses are accepted for the sake of reasoning. In Euclid's book, postulates are construction methods that assure the existence of the geometric objects. Today postulates and axioms are used as synonyms while the 18th‐century philosophy made differences: Lambert defined axioms as descriptive sentences and postulates as prescriptive sentences. According to Kant, mathematical postulates create (synthesize) concepts (Mittelstrass, 1980b ). Definitions then fix the use of signs; they can be semantic definitions that explain the proper meaning of a sign in common language use (in a dictionary style) or they can be syntactic definitions that regulate the use of these signs in formal operations. Nominal definitions explain the words, while real definitions explain the meaning or the nature of the defined object. Definitions are thus essential for the development of a language of science, assuring communication and mutual understanding (Mittelstrass, 1980c ). Finally, hypotheses are also frequently defined as consistent conjectures that are compatible with the available knowledge. The truth of the hypothesis is only supposed in order to explain true observations and facts. Consequences of this hypothetical assumptions should explain the observed facts. Normally, descriptive hypotheses precede explanatory hypotheses in the development of scientific thought. Sometimes only tentative concepts are introduced as working hypotheses to test whether they have an explanatory capacity for the observations (Mittelstrass, 1980d ).
The Euclidian geometry is constructed along a logical “if→then” concept. The “if‐clause” formulates at the beginning the supposition, the “then clause” formulates the consequences from these axioms which provides a system of geometric theorems or insights. The conclusions do not follow directly from the hypothesis; this would otherwise represent self‐evident immediate conclusions. The “if‐then” concept in geometry is not used as in other branches of science where the consequences deduced from the axioms are checked against reality whether they are true, in order to confirm the validity of the hypothesis. The task in mathematics is: what can be logically deduced from a given set of axioms to build a contradiction‐free system of geometry. Whether this applies to the real world is in contrast to the situation in natural sciences another question and absolutely secondary to mathematics (Syntopicon, 1992 ).
In his Scientific Treatises on Geometric Demonstrations , Pascal ( 1623‐1662b ) formulates “Five rules are absolutely necessary and we cannot dispense with them without an essential defect and frequently even error. Do not leave undefined any terms at all obscure or ambiguous. Use in definitions of terms only words perfectly well known or already explained. Do not fail to ask that each of the necessary principles be granted, however clear and evident it may be. Ask only that perfectly self‐evident things be granted as axioms. Prove all propositions, using for their proof only axioms that are perfectly self‐evident or propositions already demonstrated or granted. Never get caught in the ambiguity of terms by failing to substitute in thought the definitions which restrict or define them. One should accept as true only those things whose contradiction appears to be false. We may then boldly affirm the original statement, however incomprehensible it is.”
Kant ( 1724–1804 ) wrote that the analysis described in his book The Critique of Pure Reason “has now taught us that all its efforts to extend the bounds of knowledge by means of pure speculation, are utterly fruitless. So much the wider field lies open to hypothesis; as where we cannot know with certainty, we are at liberty to make guesses and to form suppositions. Imagination may be allowed, under the strict surveillance of reason, to invent suppositions; but these must be based on something that is perfectly certain‐ and that is the possibility of the object. Such a supposition is termed a hypothesis. We cannot imagine or invent any object or any property of an object not given in experience and employ it in a hypothesis; otherwise we should be basing our chain of reasoning upon mere chimerical fancies and not upon conception of things. Thus, we have no right to assume of new powers, not existing in nature and consequently we cannot assume that there is any other kind of community among substances than that observable in experience, any kind of presence than that in space and any kind of duration than that in time. The conditions of possible experience are for reason the only conditions of the possibility of things. Otherwise, such conceptions, although not self‐contradictory, are without object and without application. Transcendental hypotheses are therefore inadmissible, and we cannot use the liberty of employing in the absence of physical, hyperphysical grounds of explanation because such hypotheses do not advance reason, but rather stop it in its progress. When the explanation of natural phenomena happens to be difficult, we have constantly at hand a transcendental ground of explanation, which lifts us above the necessity of investigating nature. The next requisite for the admissibility of a hypothesis is its sufficiency. That is it must determine a priori the consequences which are given in experience and which are supposed to follow from the hypothesis itself.” Kant stresses another aspect when dealing with hypotheses: “It is our duty to try to discover new objections, to put weapons in the hands of our opponent, and to grant him the most favorable position. We have nothing to fear from these concessions; on the contrary, we may rather hope that we shall thus make ourselves master of a possession which no one will ever venture to dispute.”
For Kant's analytical and synthetical judgements and Difference between philosophy and mathematics (Kant, Whitehead) , see Appendices S1 and S2 , respectively.
The mathematician‐philosopher Poincaré ( 1854 –1912a) explored the foundation of mathematics and physics in his book Science and Hypothesis . In the preface to the book, he summarizes common thinking of scientists at the end of the 19th century. “To the superficial observer scientific truth is unassailable, the logic of science is infallible, and if scientific men sometimes make mistakes, it is because they have not understood the rules of the game. Mathematical truths are derived from a few self‐evident propositions, by a chain of flawless reasoning, they are imposed not only by us, but on Nature itself. This is for the minds of most people the origin of certainty in science.” Poincaré then continues “but upon more mature reflection the position held by hypothesis was seen; it was recognized that it is as necessary to the experimenter as it is to the mathematician. And then the doubt arose if all these constructions are built on solid foundations.” However, “to doubt everything or to believe everything are two equally convenient solutions: both dispense with the necessity of reflection. Instead, we should examine with the utmost care the role of hypothesis; we shall then recognize not only that it is necessary, but that in most cases it is legitimate. We shall also see that there are several kinds of hypotheses; that some are verifiable and when once confirmed by experiment become truths of great fertility; that others may be useful to us in fixing our ideas; and finally that others are hypotheses only in appearance, and reduce to definitions or to conventions in disguise.” Poincaré argues that “we must seek mathematical thought where it has remained pure‐i.e. in arithmetic, in the proofs of the most elementary theorems. The process is proof by recurrence. We first show that a theorem is true for n = 1; we then show that if it is true for n –1 it is true for n; and we conclude that it is true for all integers. The essential characteristic of reasoning by recurrence is that it contains, condensed in a single formula, an infinite number of syllogisms.” Syllogism is logical argument that applies deductive reasoning to arrive at a conclusion. Poincaré notes “that here is a striking analogy with the usual process of induction. But an essential difference exists. Induction applied to the physical sciences is always uncertain because it is based on the belief in a general order of the universe, an order which is external to us. Mathematical induction‐ i.e. proof by recurrence – is on the contrary, necessarily imposed on us, because it is only the affirmation of a property of the mind itself. No doubt mathematical recurrent reasoning and physical inductive reasoning are based on different foundations, but they move in parallel lines and in the same direction‐namely, from the particular to the general.”
Mathematics is an abstract science that intrinsically does not request that the structures described reflect a physical reality. Paradoxically, mathematics is the language of physics since the founder of experimental physics Galilei used Euclidian geometry when exploring the laws of the free fall. In his 1623 treatise The Assayer , Galilei ( 1564 –1642a) famously formulated that the book of Nature is written in the language of mathematics, thus establishing a link between formal concepts in mathematics and the structure of the physical world. Euclid's parallel axiom played historically a prominent role for the connection between mathematical concepts and physical realities. Mathematicians had doubted that the parallel axiom was needed and tried to prove it. In Euclidian geometry, there is a connection between the parallel axiom and the sum of the angles in a triangle being two right angles. It is therefore revealing that the famous mathematician C.F. Gauss investigated in the early 19th century experimentally whether this Euclidian theorem applies in nature. He approached this problem by measuring the sum of angles in a real triangle by using geodetic angle measurements of three geographical elevations in the vicinity of Göttingen where he was teaching mathematics. He reportedly measured a sum of the angles in this triangle that differed from 180°. Gauss had at the same time also developed statistical methods to evaluate the accuracy of measurements. Apparently, the difference of his measured angles was still within the interval of Gaussian error propagation. He did not publish the reasoning and the results for this experiment because he feared the outcry of colleagues about this unorthodox, even heretical approach to mathematical reasoning (Carnap, 1891 ‐1970a). However, soon afterwards non‐Euclidian geometries were developed. In the words of Poincaré, “Lobatschewsky assumes at the outset that several parallels may be drawn through a point to a given straight line, and he retains all the other axioms of Euclid. From these hypotheses he deduces a series of theorems between which it is impossible to find any contradiction, and he constructs a geometry as impeccable in its logic as Euclidian geometry. The theorems are very different, however, from those to which we are accustomed, and at first will be found a little disconcerting. For instance, the sum of the angles of a triangle is always less than two right angles, and the difference between that sum and two right angles is proportional to the area of the triangle. Lobatschewsky's propositions have no relation to those of Euclid, but are none the less logically interconnected.” Poincaré continues “most mathematicians regard Lobatschewsky's geometry as a mere logical curiosity. Some of them have, however, gone further. If several geometries are possible, they say, is it certain that our geometry is true? Experiments no doubt teaches us that the sum of the angles of a triangle is equal to two right angles, but this is because the triangles we deal with are too small” (Poincaré, 1854 ‐1912a)—hence the importance of Gauss' geodetic triangulation experiment. Gauss was aware that his three hills experiment was too small and thought on measurements on triangles formed with stars.
Lobatschewsky's hyperbolic geometry did not remain the only non‐Euclidian geometry. Riemann developed a geometry without the parallel axiom, while the other Euclidian axioms were maintained with the exception of that of Order (Anordnung). Poincaré notes “so there is a kind of opposition between the geometries. For instance the sum of the angles in a triangle is equal to two right angles in Euclid's geometry, less than two right angles in that of Lobatschewsky, and greater than two right angles in that of Riemann. The number of parallel lines that can be drawn through a given point to a given line is one in Euclid's geometry, none in Riemann's, and an infinite number in the geometry of Lobatschewsky. Let us add that Riemann's space is finite, although unbounded.” As further distinction, the ratio of the circumference to the diameter of a circle is equal to π in Euclid's, greater than π in Lobatschewsky's and smaller than π in Riemann's geometry. A further difference between these geometries concerns the degree of curvature (Krümmungsmass k) which is 0 for a Euclidian surface, smaller than 0 for a Lobatschewsky and greater than 0 for a Riemann surface. The difference in curvature can be roughly compared with plane, concave and convex surfaces. The inner geometric structure of a Riemann plane resembles the surface structure of a Euclidean sphere and a Lobatschewsky plane resembles that of a Euclidean pseudosphere (a negatively curved geometry of a saddle). What geometry is true? Poincaré asked “Ought we then, to conclude that the axioms of geometry are experimental truths?” and continues “If geometry were an experimental science, it would not be an exact science. The geometric axioms are therefore neither synthetic a priori intuitions as affirmed by Kant nor experimental facts. They are conventions. Our choice among all possible conventions is guided by experimental facts; but it remains free and is only limited by the necessity of avoiding contradictions. In other words, the axioms of geometry are only definitions in disguise. What then are we to think of the question: Is Euclidean geometry true? It has no meaning. One geometry cannot be more true than another, it can only be more convenient. Now, Euclidean geometry is, and will remain, the most convenient, 1 st because it is the simplest and 2 nd because it sufficiently agrees with the properties of natural bodies” (Poincaré, 1854 ‐1912a).
Poincaré's book was published in 1903 and only a few years later Einstein published his general theory of relativity ( 1916 ) where he used a non‐Euclidean, Riemann geometry and where he demonstrated a structure of space that deviated from Euclidean geometry in the vicinity of strong gravitational fields. And in 1919, astronomical observations during a solar eclipse showed that light rays from a distant star were indeed “bent” when passing next to the sun. These physical observations challenged the view of Poincaré, and we should now address some aspects of hypotheses in physics (Carnap, 1891 ‐1970b).
The long life of the five elements hypothesis.
Physical sciences—not to speak of biological sciences — were less developed in antiquity than mathematics which is already demonstrated by the primitive ideas on the elements constituting physical bodies. Plato and Aristotle spoke of the four elements which they took over from Thales (water), Anaximenes (air) and Parmenides (fire and earth) and add a fifth element (quinta essentia, our quintessence), namely ether. Ether is imagined a heavenly element belonging to the supralunar world. In Plato's dialogue Timaios (Plato, c.424‐c.348 BC a ), the five elements were associated with regular polyhedra in geometry and became known as Platonic bodies: tetrahedron (fire), octahedron (air), cube (earth), icosahedron (water) and dodecahedron (ether). In regular polyhedra, faces are congruent (identical in shape and size), all angles and all edges are congruent, and the same number of faces meet at each vertex. The number of elements is limited to five because in Euclidian space there are exactly five regular polyhedral. There is in Plato's writing even a kind of geometrical chemistry. Since two octahedra (air) plus one tetrahedron (fire) can be combined into one icosahedron (water), these “liquid” elements can combine while this is not the case for combinations with the cube (earth). The 12 faces of the dodecahedron were compared with the 12 zodiac signs (Mittelstrass, 1980e ). This geometry‐based hypothesis of physics had a long life. As late as 1612, Kepler in his Mysterium cosmographicum tried to fit the Platonic bodies into the planetary shells of his solar system model. The ether theory even survived into the scientific discussion of the 19th‐century physics and the idea of a mathematical structure of the universe dominated by symmetry operations even fertilized 20th‐century ideas about symmetry concepts in the physics of elementary particles.
The ether hypothesis figures prominently in the 1690 Treatise on Light from Huygens ( 1617‐1670 ). He first reports on the transmission of sound by air when writing “this may be proved by shutting up a sounding body in a glass vessel from which the air is withdrawn and care was taken to place the sounding body on cotton that it cannot communicate its tremor to the glass vessel which encloses it. After having exhausted all the air, one hears no sound from the metal though it is struck.” Huygens comes up with some foresight when suspecting “the air is of such a nature that it can be compressed and reduced to a much smaller space than that it normally occupies. Air is made up of small bodies which float about and which are agitated very rapidly. So that the spreading of sound is the effort which these little bodies make in collisions with one another, to regain freedom when they are a little more squeezed together in the circuit of these waves than elsewhere.”
“That is not the same air but another kind of matter in which light spreads; since if the air is removed from the vessel the light does not cease to traverse it as before. The extreme velocity of light cannot admit such a propagation of motion” as sound waves. To achieve the propagation of light, Huygens invokes ether “as a substance approaching to perfect hardness and possessing springiness as prompt as we choose. One may conceive light to spread successively by spherical waves. The propagation consists nowise in the transport of those particles but merely in a small agitation which they cannot help communicate to those surrounding.” The hypothesis of an ether in outer space fills libraries of physical discussions, but all experimental approaches led to contradictions with respect to postulated properties of this hypothetical material for example when optical experiments showed that light waves display transversal and not longitudinal oscillations.
Mechanical models for the transmission of light or gravitation waves requiring ether were finally put to rest by the theory of relativity from Einstein (Mittelstrass, 1980f ). This theory posits that the speed of light in an empty space is constant and does not depend on movements of the source of light or that of an observer as requested by the ether hypothesis. The theory of relativity also provides an answer how the force of gravitation is transmitted from one mass to another across an essentially empty space. In the non‐Euclidian formulation of the theory of relativity (Einstein used the Riemann geometry), there is no gravitation force in the sense of mechanical or electromagnetic forces. The gravitation force is in this formulation simply replaced by a geometric structure (space curvature near high and dense masses) of a four‐dimensional space–time system (Carnap, 1891 ‐1970c; Einstein & Imfeld, 1956 ) Gravitation waves and gravitation lens effects have indeed been experimental demonstrated by astrophysicists (Dorfmüller et al., 1998 ).
For Aristotle's on physical hypotheses , see Appendix S3 .
In the following, the opinions of a number of famous scientists and philosophers on hypotheses are quoted to provide a historical overview on the subject.
In his book Revolutions of Heavenly Spheres Copernicus ( 1473–1543 ) reasoned in the preface about hypotheses in physics. “Since the newness of the hypotheses of this work ‐which sets the earth in motion and puts an immovable sun at the center of the universe‐ has already received a great deal of publicity, I have no doubt that certain of the savants have taken great offense.” He defended his heliocentric thesis by stating “For it is the job of the astronomer to use painstaking and skilled observations in gathering together the history of the celestial movements‐ and then – since he cannot by any line of reasoning reach the true causes of these movements‐ to think up or construct whatever causes or hypotheses he pleases such that, by the assumption of these causes, those same movements can be calculated from the principles of geometry for the past and the future too. This artist is markedly outstanding in both of these respects: for it is not necessary that these hypotheses should be true, or even probable; but it is enough if they provide a calculus which fits the observations.” This preface written in 1543 sounds in its arguments very modern physics. However, historians of science have discovered that it was probably written by a theologian friend of Copernicus to defend the book against the criticism by the church.
In his book Novum Organum , Francis Bacon ( 1561–1626 ) claims for hypotheses and scientific reasoning “that they augur well for the sciences, when the ascent shall proceed by a true scale and successive steps, without interruption or breach, from particulars to the lesser axioms, thence to the intermediates and lastly to the most general.” He then notes “that the lowest axioms differ but little from bare experiments, the highest and most general are notional, abstract, and of no real weight. The intermediate are true, solid, full of life, and up to them depend the business and fortune of mankind.” He warns that “we must not then add wings, but rather lead and ballast to the understanding, to prevent its jumping and flying, which has not yet been done; but whenever this takes place we may entertain greater hopes of the sciences.” With respect to methodology, Bacon claims that “we must invent a different form of induction. The induction which proceeds by simple enumeration is puerile, leads to uncertain conclusions, …deciding generally from too small a number of facts. Sciences should separate nature by proper rejections and exclusions and then conclude for the affirmative, after collecting a sufficient number of negatives.”
William Gilbert introduced in his book On the Loadstone (Gilbert, 1544‐1603 ) the argument of plausibility into physical hypothesis building. “From these arguments, therefore, we infer not with mere probability, but with certainty, the diurnal rotation of the earth; for nature ever acts with fewer than with many means; and because it is more accordant to reason that the one small body, the earth, should make a daily revolution than the whole universe should be whirled around it.”
Descartes ( 1596‐1650 ) reflected on the sources of understanding in his book Rules for Direction and distinguished what “comes about by impulse, by conjecture, or by deduction. Impulse can assign no reason for their belief and when determined by fanciful disposition, it is almost always a source of error.” When speaking about the working of conjectures he quotes thoughts of Aristotle: “water which is at a greater distance from the center of the globe than earth is likewise less dense substance, and likewise the air which is above the water, is still rarer. Hence, we hazard the guess that above the air nothing exists but a very pure ether which is much rarer than air itself. Moreover nothing that we construct in this way really deceives, if we merely judge it to be probable and never affirm it to be true; in fact it makes us better instructed. Deduction is thus left to us as the only means of putting things together so as to be sure of their truth. Yet in it, too, there may be many defects.”
Locke ( 1632‐1704 ) in his treatise Concerning Human Understanding admits that “we may make use of any probable hypotheses whatsoever. Hypotheses if they are well made are at least great helps to the memory and often direct us to new discoveries. However, we should not take up any one too hastily.” Also, practising scientists argued against careless use of hypotheses and proposed remedies. Lavoisier ( 1743‐1794 ) in the preface to his Element of Chemistry warned about beaten‐track hypotheses. “Instead of applying observation to the things we wished to know, we have chosen rather to imagine them. Advancing from one ill‐founded supposition to another, we have at last bewildered ourselves amidst a multitude of errors. These errors becoming prejudices, are adopted as principles and we thus bewilder ourselves more and more. We abuse words which we do not understand. There is but one remedy: this is to forget all that we have learned, to trace back our ideas to their sources and as Bacon says to frame the human understanding anew.”
Faraday ( 1791–1867 ) in a Speculation Touching Electric Conduction and the Nature of Matter highlighted the fundamental difference between hypotheses and facts when noting “that he has most power of penetrating the secrets of nature, and guessing by hypothesis at her mode of working, will also be most careful for his own safe progress and that of others, to distinguish that knowledge which consists of assumption, by which I mean theory and hypothesis, from that which is the knowledge of facts and laws; never raising the former to the dignity or authority of the latter.”
Darwin ( 1809 –1882a) defended the conclusions and hypothesis of his book The Origin of Species “that species have been modified in a long course of descent. This has been affected chiefly through the natural selection of numerous, slight, favorable variations.” He uses a post hoc argument for this hypothesis: “It can hardly be supposed that a false theory would explain, to so satisfactory a manner as does the theory of natural selection, the several large classes of facts” described in his book.
In the concluding chapter of The Descent of Man Darwin ( 1809 –1882b) admits “that many of the views which have been advanced in this book are highly speculative and some no doubt will prove erroneous.” However, he distinguished that “false facts are highly injurious to the progress of science for they often endure long; but false views do little harm for everyone takes a salutory pleasure in proving their falseness; and when this is done, one path to error is closed and the road to truth is often at the same time opened.”
The American philosopher William James ( 1842–1907 ) concurred with Darwin's view when he wrote in his Principles of Psychology “every scientific conception is in the first instance a spontaneous variation in someone'’s brain. For one that proves useful and applicable there are a thousand that perish through their worthlessness. The scientific conceptions must prove their worth by being verified. This test, however, is the cause of their preservation, not of their production.”
The American philosopher J. Dewey ( 1859‐1952 ) in his treatise Experience and Education notes that “the experimental method of science attaches more importance not less to ideas than do other methods. There is no such thing as experiment in the scientific sense unless action is directed by some leading idea. The fact that the ideas employed are hypotheses, not final truths, is the reason why ideas are more jealously guarded and tested in science than anywhere else. As fixed truths they must be accepted and that is the end of the matter. But as hypotheses, they must be continuously tested and revised, a requirement that demands they be accurately formulated. Ideas or hypotheses are tested by the consequences which they produce when they are acted upon. The method of intelligence manifested in the experimental method demands keeping track of ideas, activities, and observed consequences. Keeping track is a matter of reflective review.”
James ( 1842‐1907 ) pushed this idea further when saying “Scientific thought goes by selection. We break the solid plenitude of fact into separate essences, conceive generally what only exists particularly, and by our classifications leave nothing in its natural neighborhood. The reality exists as a plenum. All its part are contemporaneous, but we can neither experience nor think this plenum. What we experience is a chaos of fragmentary impressions, what we think is an abstract system of hypothetical data and laws. We must decompose each chaos into single facts. We must learn to see in the chaotic antecedent a multitude of distinct antecedents, in the chaotic consequent a multitude of distinct consequents.” From these considerations James concluded “even those experiences which are used to prove a scientific truth are for the most part artificial experiences of the laboratory gained after the truth itself has been conjectured. Instead of experiences engendering the inner relations, the inner relations are what engender the experience here.“
Freud ( 1856–1939 ) considered curiosity and imagination as driving forces of hypothesis building which need to be confronted as quickly as possible with observations. In Beyond the Pleasure Principle , Freud wrote “One may surely give oneself up to a line of thought and follow it up as far as it leads, simply out of scientific curiosity. These innovations were direct translations of observation into theory, subject to no greater sources of error than is inevitable in anything of the kind. At all events there is no way of working out this idea except by combining facts with pure imagination and thereby departing far from observation.” This can quickly go astray when trusting intuition. Freud recommends “that one may inexorably reject theories that are contradicted by the very first steps in the analysis of observation and be aware that those one holds have only a tentative validity.”
The geneticist Waddington ( 1905–1975 ) in his essay The Nature of Life states that “a scientific theory cannot remain a mere structure within the world of logic, but must have implications for action and that in two rather different ways. It must involve the consequence that if you do so and so, such and such result will follow. That is to say it must give, or at least offer, the possibility of controlling the process. Secondly, its value is quite largely dependent on its power of suggesting the next step in scientific advance. Any complete piece of scientific work starts with an activity essentially the same as that of an artist. It starts by asking a relevant question. The first step may be a new awareness of some facet of the world that no one else had previously thought worth attending to. Or some new imaginative idea which depends on a sensitive receptiveness to the oddity of nature essentially similar to that of the artist. In his logical analysis and manipulative experimentation, the scientist is behaving arrogantly towards nature, trying to force her into his categories of thought or to trick her into doing what he wants. But finally he has to be humble. He has to take his intuition, his logical theory and his manipulative skill to the bar of Nature and see whether she answers yes or no; and he has to abide by the result. Science is often quite ready to tolerate some logical inadequacy in a theory‐or even a flat logical contradiction like that between the particle and wave theories of matter‐so long as it finds itself in the possession of a hypothesis which offers both the possibility of control and a guide to worthwhile avenues of exploration.”
Poincaré ( 1854 –1912b) also dealt with physics in Science and Hypothesis . “Experiment is the sole source of truth. It alone can teach us certainty. Cannot we be content with experiment alone? What place is left for mathematical physics? The man of science must work with method. Science is built up of facts, as a house is built of stones, but an accumulation of facts is no more a science than a heap of stones is a house. It is often said that experiments should be made without preconceived concepts. That is impossible. Without the hypothesis, no conclusion could have been drawn; nothing extraordinary would have been seen; and only one fact the more would have been catalogued, without deducing from it the remotest consequence.” Poincaré compares science to a library. Experimental physics alone can enrich the library with new books, but mathematical theoretical physics draw up the catalogue to find the books and to reveal gaps which have to be closed by the purchase of new books.
Poincaré continues “we all know that there are good and bad experiments. The latter accumulate in vain. Whether there are hundred or thousand, one single piece of work will be sufficient to sweep them into oblivion. Bacon invented the term of an experimentum crucis for such experiments. What then is a good experiment? It is that which teaches us something more than an isolated fact. It is that which enables us to predict and to generalize. Experiments only gives us a certain number of isolated points. They must be connected by a continuous line and that is true generalization. Every generalization is a hypothesis. It should be as soon as possible submitted to verification. If it cannot stand the test, it must be abandoned without any hesitation. The physicist who has just given up one of his hypotheses should rejoice, for he found an unexpected opportunity of discovery. The hypothesis took into account all the known factors which seem capable of intervention in the phenomenon. If it is not verified, it is because there is something unexpected. Has the hypothesis thus rejected been sterile? Far from it. It has rendered more service than a true hypothesis.” Poincaré notes that “with a true hypothesis only one fact the more would have been catalogued, without deducing from it the remotest consequence. It may be said that the wrong hypothesis has rendered more service than a true hypothesis.” However, Poincaré warns that “some hypotheses are dangerous – first and foremost those which are tacit and unconscious. And since we make them without knowing them, we cannot get rid of them.” Poincaré notes that here mathematical physics is of help because by its precision one is compelled to formulate all the hypotheses, revealing also the tacit ones.
Poincaré also warned against multiplying hypotheses indefinitely: “If we construct a theory upon multiple hypotheses, and if experiment condemns it, which of the premisses must be changed?” Poincaré also recommended to “resolve the complex phenomenon given directly by experiment into a very large number of elementary phenomena. First, with respect to time. Instead of embracing in its entirety the progressive development of a phenomenon, we simply try to connect each moment with the one immediately preceding. Next, we try to decompose the phenomenon in space. We must try to deduce the elementary phenomenon localized in a very small region of space.” Poincaré suggested that the physicist should “be guided by the instinct of simplicity, and that is why in physical science generalization so readily takes the mathematical form to state the problem in the form of an equation.” This argument goes back to Galilei ( 1564 –1642b) who wrote in The Two Sciences “when I observe a stone initially at rest falling from an elevated position and continually acquiring new increments of speed, why should I not believe that such increases take place in a manner which is exceedingly simple and rather obvious to everybody? If now we examine the matter carefully we find no addition or increment more simple than that which repeats itself always in the same manner. It seems we shall not be far wrong if we put the increment of speed as proportional to the increment of time.” With a bit of geometrical reasoning, Galilei deduced that the distance travelled by a freely falling body varies as the square of the time. However, Galilei was not naïve and continued “I grant that these conclusions proved in the abstract will be different when applied in the concrete” and considers disturbances cause by friction and air resistance that complicate the initially conceived simplicity.
Some philosophers of science attributed a fundamental importance to observations for the acquisition of experience in science. The process starts with accidental observations (Aristotle), going to systematic observations (Bacon), leading to quantitative rules obtained with exact measurements (Newton and Kant) and culminating in observations under artificially created conditions in experiments (Galilei) (Mittelstrass, 1980g ).
In fact, Newton wrote that he had developed his theory of gravitation from experience followed by induction. K. Popper ( 1902‐1994 ) in his book Conjectures and Refutations did not agree with this logical flow “experience leading to theory” and that for several reasons. This scheme is according to Popper intuitively false because observations are always inexact, while theory makes absolute exact assertions. It is also historically false because Copernicus and Kepler were not led to their theories by experimental observations but by geometry and number theories of Plato and Pythagoras for which they searched verifications in observational data. Kepler, for example, tried to prove the concept of circular planetary movement influenced by Greek theory of the circle being a perfect geometric figure and only when he could not demonstrate this with observational data, he tried elliptical movements. Popper noted that it was Kant who realized that even physical experiments are not prior to theories when quoting Kant's preface to the Critique of Pure Reason : “When Galilei let his globes run down an inclined plane with a gravity which he has chosen himself, then a light dawned on all natural philosophers. They learnt that our reason can only understand what it creates according to its own design; that we must compel Nature to answer our questions, rather than cling to Nature's apron strings and allow her to guide us. For purely accidental observations, made without any plan having been thought out in advance, cannot be connected by a law‐ which is what reason is searching for.” From that reasoning Popper concluded that “we ourselves must confront nature with hypotheses and demand a reply to our questions; and that lacking such hypotheses, we can only make haphazard observations which follow no plan and which can therefore never lead to a natural law. Everyday experience, too, goes far beyond all observations. Everyday experience must interpret observations for without theoretical interpretation, observations remain blind and uninformative. Everyday experience constantly operates with abstract ideas, such as that of cause and effect, and so it cannot be derived from observation.” Popper agreed with Kant who said “Our intellect does not draw its laws from nature…but imposes them on nature”. Popper modifies this statement to “Our intellect does not draw its laws from nature, but tries‐ with varying degrees of success – to impose upon nature laws which it freely invents. Theories are seen to be free creations of our mind, the result of almost poetic intuition. While theories cannot be logically derived from observations, they can, however, clash with observations. This fact makes it possible to infer from observations that a theory is false. The possibility of refuting theories by observations is the basis of all empirical tests. All empirical tests are therefore attempted refutations.”
Is biology special.
Waddington notes that “living organisms are much more complicated than the non‐living things. Biology has therefore developed more slowly than sciences such as physics and chemistry and has tended to rely on them for many of its basic ideas. These older physical sciences have provided biology with many firm foundations which have been of the greatest value to it, but throughout most of its history biology has found itself faced with the dilemma as to how far its reliance on physics and chemistry should be pushed” both with respect to its experimental methods and its theoretical foundations. Vitalism is indeed such a theory maintaining that organisms cannot be explained solely by physicochemical laws claiming specific biological forces active in organisms. However, efforts to prove the existence of such vital forces have failed and today most biologists consider vitalism a superseded theory.
Biology as a branch of science is as old as physics. If one takes Aristotle as a reference, he has written more on biology than on physics. Sophisticated animal experiments were already conducted in the antiquity by Galen (Brüssow, 2022 ). Alertus Magnus displayed biological research interest during the medieval time. Knowledge on plants provided the basis of medical drugs in early modern times. What explains biology's decreasing influence compared with the rapid development of physics by Galilei and Newton? One reason is the possibility to use mathematical equations to describe physical phenomena which was not possible for biological phenomena. Physics has from the beginning displayed a trend to few fundamental underlying principles. This is not the case for biology. With the discovery of new continents, biologists were fascinated by the diversity of life. Diversity was the conducting line of biological thinking. This changed only when taxonomists and comparative anatomists revealed recurring pattern in this stunning biological variety and when Darwin provided a theoretical concept to understand variation as a driving force in biology. Even when genetics and molecular biology allowed to understand biology from a few universally shared properties, such as a universal genetic code, biology differed in fundamental aspects from physics and chemistry. First, biology is so far restricted to the planet earth while the laws of physic and chemistry apply in principle to the entire universe. Second, biology is to a great extent a historical discipline; many biological processes cannot be understood from present‐day observations because they are the result of historical developments in evolution. Hence, the importance of Dobzhansky's dictum that nothing makes sense in biology except in the light of evolution. The great diversity of life forms, the complexity of processes occurring in cells and their integration in higher organisms and the importance of a historical past for the understanding of extant organisms, all that has delayed the successful application of mathematical methods in biology or the construction of theoretical frameworks in biology. Theoretical biology by far did not achieve a comparable role as theoretical physics which is on equal foot with experimental physics. Many biologists are even rather sceptical towards a theoretical biology and see progress in the development of ever more sophisticated experimental methods instead in theoretical concepts expressed by new hypotheses.
Philosophers distinguish rational knowledge ( cognitio ex principiis ) from knowledge from data ( cognitio ex data ). Kant associates these two branches with natural sciences and natural history, respectively. The latter with descriptions of natural objects as prominently done with systematic classification of animals and plants or, where it is really history, when describing events in the evolution of life forms on earth. Cognitio ex data thus played a much more prominent role in biology than in physics and explains why the compilation of data and in extremis the collection of museum specimen characterizes biological research. To account for this difference, philosophers of the logical empiricism developed a two‐level concept of science languages consisting of a language of observations (Beobachtungssprache) and a language of theories (Theoriesprache) which are linked by certain rules of correspondence (Korrespondenzregeln) (Carnap, 1891 –1970d). If one looks into leading biological research journals, it becomes clear that biology has a sophisticated language of observation and a much less developed language of theories.
Do we need more philosophical thinking in biology or at least a more vigorous theoretical biology? The breathtaking speed of progress in experimental biology seems to indicate that biology can well develop without much theoretical or philosophical thinking. At the same time, one could argue that some fields in biology might need more theoretical rigour. Microbiologists might think on microbiome research—one of the breakthrough developments of microbiology research in recent years. The field teems with fascinating, but ill‐defined terms (our second genome; holobionts; gut–brain axis; dysbiosis, symbionts; probiotics; health benefits) that call for stricter definitions. One might also argue that biologists should at least consider the criticism of Goethe ( 1749–1832 ), a poet who was also an active scientist. In Faust , the devil ironically teaches biology to a young student.
“Wer will was Lebendigs erkennen und beschreiben, Sucht erst den Geist herauszutreiben, Dann hat er die Teile in seiner Hand, Fehlt, leider! nur das geistige Band.” (To docket living things past any doubt. You cancel first the living spirit out: The parts lie in the hollow of your hand, You only lack the living thing you banned).
We probably need both in biology: more data and more theory and hypotheses.
The author reports no conflict of interest.
No funding information provided.
Appendix S1
Brüssow, H. (2022) On the role of hypotheses in science . Microbial Biotechnology , 15 , 2687–2698. Available from: 10.1111/1751-7915.14141 [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
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The “leafing intensity premium” hypothesis and the scaling relationships of the functional traits of bamboo species.
2. materials and methods, 2.1. sampling site and data acquisition, 2.2. data analysis, 4. discussion, 4.1. scaling relationship between tlm and tnlm, 4.2. scaling relationships between mlm and leafing intensity, 4.3. different metrics of leafing intensity, 5. conclusions, supplementary materials, author contributions, data availability statement, acknowledgments, conflicts of interest.
Click here to enlarge figure
Latin Name | Leaf Length (cm) | Total Number of Leaves | Total Leaf Fresh Mass (g) | Culm Fresh Mass (g) | Culm Height (cm) |
---|---|---|---|---|---|
Indocalamus barbatus | 14.7 ± 4.2 | 21.4 ± 13.6 | 6.83 ± 4.00 | 18.7 ± 8.7 | 88.8 ± 26.6 |
Indocalamus pedalis | 18.4 ± 5.6 | 11.0 ± 6.2 | 6.53 ± 3.90 | 18.1 ± 9.80 | 71.6 ± 23.2 |
Indocalamus pumilus | 14.0 ± 4.1 | 23.4 ± 13.2 | 7.80 ± 4.42 | 19.7 ± 13.2 | 68.1 ± 35.4 |
Indocalamus victorialis | 17.0 ± 4.3 | 14.2 ± 9.8 | 10.6 ± 6.42 | 29.2 ± 14.5 | 76.5 ± 23.5 |
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Yao, W.; Shi, P.; Wang, J.; Mu, Y.; Cao, J.; Niklas, K.J. The “Leafing Intensity Premium” Hypothesis and the Scaling Relationships of the Functional Traits of Bamboo Species. Plants 2024 , 13 , 2340. https://doi.org/10.3390/plants13162340
Yao W, Shi P, Wang J, Mu Y, Cao J, Niklas KJ. The “Leafing Intensity Premium” Hypothesis and the Scaling Relationships of the Functional Traits of Bamboo Species. Plants . 2024; 13(16):2340. https://doi.org/10.3390/plants13162340
Yao, Weihao, Peijian Shi, Jinfeng Wang, Youying Mu, Jiajie Cao, and Karl J. Niklas. 2024. "The “Leafing Intensity Premium” Hypothesis and the Scaling Relationships of the Functional Traits of Bamboo Species" Plants 13, no. 16: 2340. https://doi.org/10.3390/plants13162340
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A research hypothesis (also called a scientific hypothesis) is a statement about the expected outcome of a study (for example, a dissertation or thesis). To constitute a quality hypothesis, the statement needs to have three attributes - specificity, clarity and testability. Let's take a look at these more closely.
HYPOTHESIS TESTING. A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the "alternate" hypothesis, and the opposite ...
It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis. 7.
A snapshot analysis of citation activity of hypothesis articles may reveal interest of the global scientific community towards their implications across various disciplines and countries. As a prime example, Strachan's hygiene hypothesis, published in 1989,10 is still attracting numerous citations on Scopus, the largest bibliographic database ...
Definition: Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation. Hypothesis is often used in scientific research to guide the design of experiments ...
INTRODUCTION. Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses.1,2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results.3,4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the ...
A hypothesis (from the Greek, foundation) is a logical construct, interposed between a problem and its solution, which represents a proposed answer to a research question. It gives direction to the investigator's thinking about the problem and, therefore, facilitates a solution. Unlike facts and assumptions (presumed true and, therefore, not ...
A research hypothesis, in its plural form "hypotheses," is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question. A hypothesis is not just a guess. It should be based on ...
The procedure for hypothesis testing is undertaken for making a choice between the rejection and acceptance of a null hypothesis observing the following steps: Setting up of hypothesis consists of the data that makes the statement of a null hypothesis, which should clearly state the nature of the research problem;
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question. A hypothesis is not just a guess — it should be based on ...
A hypothesis is a prediction of what will be found at the outcome of a research project and is typically focused on the relationship between two different variables studied in the research. It is usually based on both theoretical expectations about how things work and already existing scientific evidence. Within social science, a hypothesis can ...
A hypothesis is a statement of the researcher's expectation or prediction about relationship among study variables. The research process begins and ends with the hypothesis. It is core to the ...
In these descriptions, a hypothesis was defined as one of five types: hypothesis as an assumption, hypothesis as a prediction, hypothesis as a tentative explanation, hypothesis as a tentative law, and hypothesis as a tentative causal explanation. Most scholars agreed that a hypothesis is a proposition or a set of propositions proposed as an….
hypothesis: [noun] an assumption or concession made for the sake of argument. an interpretation of a practical situation or condition taken as the ground for action.
Students learned that it is important that a good hypothesis makes a claim about the relationship between two variables, and that this relationship is specific and testable in a measurable way. Students also learned that only one variable—the independent variable—can differ between test groups. Finally, we talked about how it is important ...
2. Complex Hypothesis: A Complex hypothesis examines relationship between two or more independent variables and two or more dependent variables. 3. Working or Research Hypothesis: A research hypothesis is a specific, clear prediction about the possible outcome of a scientific research study based on specific factors of the population. 4.
Abstract. Statistical hypothesis testing is common in research, but a conventional understanding sometimes leads to mistaken application and misinterpretation. The logic of hypothesis testing presented in this article provides for a clearer understanding, application, and interpretation. Key conclusions are that (a) the magnitude of an estimate ...
Scientists are commonly taught to frame their experiments with a "hypothesis"—an idea or postulate that must be phrased as a statement of fact, so that it can be subjected to falsification. The hypothesis is constructed in advance of the experiment; it is therefore unproven in its original form. The very idea of "proof" of a ...
Merriam Webster defines a hypothesis as "an assumption or concession made for the sake of argument.". In other words, a hypothesis is an educated guess. Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it's true or not.
Scientific research progresses by the dialectic dialogue between hypothesis building and the experimental testing of these hypotheses. Microbiologists as biologists in general can rely on an increasing set of sophisticated experimental methods for hypothesis testing such that many scientists maintain that progress in biology essentially comes with new experimental tools.
Once the overwhelming majority of scientists agree with a hypothesis, meaning it has withstood the test of time and science, it becomes a theory. A theory is a tested and documented explanation of ...
Definition of Research Research comprises defining and redefining problems, formulating hypothesis or suggested solutions; collecting, ... scholars and other researchers
The "leafing intensity premium" hypothesis proposes that leaf size results from natural selection acting on different leafing intensities, i.e., the number of leaves per unit shoot volume or mass. The scaling relationships among various above-ground functional traits in the context of this hypothesis are important for understanding plant growth and ecology.
Google Scholar. Almeida H., Campello M., & Weisbach M. S. (2004). The cash flow sensitivity of cash. The Journal of Finance, 59 ... International diversification and firm performance: The S-curve hypothesis. Academy of Management Journal, 47(4), 598H-609H. Crossref. Web of Science. Google Scholar. Machokoto M., & Areneke G. (2021). Is the ...