hypothesis one or two tailed

• Skip to primary navigation
• Skip to main content
• Skip to primary sidebar

Institute for Digital Research and Education

FAQ: What are the differences between one-tailed and two-tailed tests?

When you conduct a test of statistical significance, whether it is from a correlation, an ANOVA, a regression or some other kind of test, you are given a p-value somewhere in the output.  If your test statistic is symmetrically distributed, you can select one of three alternative hypotheses. Two of these correspond to one-tailed tests and one corresponds to a two-tailed test.  However, the p-value presented is (almost always) for a two-tailed test.  But how do you choose which test?  Is the p-value appropriate for your test? And, if it is not, how can you calculate the correct p-value for your test given the p-value in your output?  

What is a two-tailed test?

First let’s start with the meaning of a two-tailed test.  If you are using a significance level of 0.05, a two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction.  This means that .025 is in each tail of the distribution of your test statistic. When using a two-tailed test, regardless of the direction of the relationship you hypothesize, you are testing for the possibility of the relationship in both directions.  For example, we may wish to compare the mean of a sample to a given value x using a t-test.  Our null hypothesis is that the mean is equal to x . A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x . The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.     

What is a one-tailed test?

Next, let’s discuss the meaning of a one-tailed test.  If you are using a significance level of .05, a one-tailed test allots all of your alpha to testing the statistical significance in the one direction of interest.  This means that .05 is in one tail of the distribution of your test statistic. When using a one-tailed test, you are testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction.  Let’s return to our example comparing the mean of a sample to a given value x using a t-test.  Our null hypothesis is that the mean is equal to x . A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x , but not both. Then, depending on the chosen tail, the mean is significantly greater than or less than x if the test statistic is in the top 5% of its probability distribution or bottom 5% of its probability distribution, resulting in a p-value less than 0.05.  The one-tailed test provides more power to detect an effect in one direction by not testing the effect in the other direction. A discussion of when this is an appropriate option follows.   

When is a one-tailed test appropriate?

Because the one-tailed test provides more power to detect an effect, you may be tempted to use a one-tailed test whenever you have a hypothesis about the direction of an effect. Before doing so, consider the consequences of missing an effect in the other direction.  Imagine you have developed a new drug that you believe is an improvement over an existing drug.  You wish to maximize your ability to detect the improvement, so you opt for a one-tailed test. In doing so, you fail to test for the possibility that the new drug is less effective than the existing drug.  The consequences in this example are extreme, but they illustrate a danger of inappropriate use of a one-tailed test.

So when is a one-tailed test appropriate? If you consider the consequences of missing an effect in the untested direction and conclude that they are negligible and in no way irresponsible or unethical, then you can proceed with a one-tailed test. For example, imagine again that you have developed a new drug. It is cheaper than the existing drug and, you believe, no less effective.  In testing this drug, you are only interested in testing if it less effective than the existing drug.  You do not care if it is significantly more effective.  You only wish to show that it is not less effective. In this scenario, a one-tailed test would be appropriate. 

When is a one-tailed test NOT appropriate?

Choosing a one-tailed test for the sole purpose of attaining significance is not appropriate.  Choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not appropriate, no matter how "close" to significant the two-tailed test was.  Using statistical tests inappropriately can lead to invalid results that are not replicable and highly questionable–a steep price to pay for a significance star in your results table!   

Deriving a one-tailed test from two-tailed output

The default among statistical packages performing tests is to report two-tailed p-values.  Because the most commonly used test statistic distributions (standard normal, Student’s t) are symmetric about zero, most one-tailed p-values can be derived from the two-tailed p-values.   

Below, we have the output from a two-sample t-test in Stata.  The test is comparing the mean male score to the mean female score.  The null hypothesis is that the difference in means is zero.  The two-sided alternative is that the difference in means is not zero.  There are two one-sided alternatives that one could opt to test instead: that the male score is higher than the female score (diff  > 0) or that the female score is higher than the male score (diff < 0).  In this instance, Stata presents results for all three alternatives.  Under the headings Ha: diff < 0 and Ha: diff > 0 are the results for the one-tailed tests. In the middle, under the heading Ha: diff != 0 (which means that the difference is not equal to 0), are the results for the two-tailed test. 

Two-sample t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- male | 91 50.12088 1.080274 10.30516 47.97473 52.26703 female | 109 54.99083 .7790686 8.133715 53.44658 56.53507 ---------+-------------------------------------------------------------------- combined | 200 52.775 .6702372 9.478586 51.45332 54.09668 ---------+-------------------------------------------------------------------- diff | -4.869947 1.304191 -7.441835 -2.298059 ------------------------------------------------------------------------------ Degrees of freedom: 198 Ho: mean(male) - mean(female) = diff = 0 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 t = -3.7341 t = -3.7341 t = -3.7341 P < t = 0.0001 P > |t| = 0.0002 P > t = 0.9999

Note that the test statistic, -3.7341, is the same for all of these tests.  The two-tailed p-value is P > |t|. This can be rewritten as P(>3.7341) + P(< -3.7341).  Because the t-distribution is symmetric about zero, these two probabilities are equal: P > |t| = 2 *  P(< -3.7341).  Thus, we can see that the two-tailed p-value is twice the one-tailed p-value for the alternative hypothesis that (diff < 0).  The other one-tailed alternative hypothesis has a p-value of P(>-3.7341) = 1-(P<-3.7341) = 1-0.0001 = 0.9999.   So, depending on the direction of the one-tailed hypothesis, its p-value is either 0.5*(two-tailed p-value) or 1-0.5*(two-tailed p-value) if the test statistic symmetrically distributed about zero. 

In this example, the two-tailed p-value suggests rejecting the null hypothesis of no difference. Had we opted for the one-tailed test of (diff > 0), we would fail to reject the null because of our choice of tails. 

The output below is from a regression analysis in Stata.  Unlike the example above, only the two-sided p-values are presented in this output.

Source | SS df MS Number of obs = 200 -------------+------------------------------ F( 2, 197) = 46.58 Model | 7363.62077 2 3681.81039 Prob > F = 0.0000 Residual | 15572.5742 197 79.0486001 R-squared = 0.3210 -------------+------------------------------ Adj R-squared = 0.3142 Total | 22936.195 199 115.257261 Root MSE = 8.8909 ------------------------------------------------------------------------------ socst | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- science | .2191144 .0820323 2.67 0.008 .0573403 .3808885 math | .4778911 .0866945 5.51 0.000 .3069228 .6488594 _cons | 15.88534 3.850786 4.13 0.000 8.291287 23.47939 ------------------------------------------------------------------------------

For each regression coefficient, the tested null hypothesis is that the coefficient is equal to zero.  Thus, the one-tailed alternatives are that the coefficient is greater than zero and that the coefficient is less than zero. To get the p-value for the one-tailed test of the variable science having a coefficient greater than zero, you would divide the .008 by 2, yielding .004 because the effect is going in the predicted direction. This is P(>2.67). If you had made your prediction in the other direction (the opposite direction of the model effect), the p-value would have been 1 – .004 = .996.  This is P(<2.67). For all three p-values, the test statistic is 2.67. 

Your Name (required)

Your Email (must be a valid email for us to receive the report!)

Comment/Error Report (required)

How to cite this page

• © 2021 UC REGENTS

• Study Guides
• One- and Two-Tailed Tests
• Method of Statistical Inference
• Types of Statistics
• Steps in the Process
• Making Predictions
• Comparing Results
• Probability
• Quiz: Introduction to Statistics
• What Are Statistics?
• Quiz: Bar Chart
• Quiz: Pie Chart
• Introduction to Graphic Displays
• Quiz: Dot Plot
• Quiz: Introduction to Graphic Displays
• Frequency Histogram
• Relative Frequency Histogram
• Quiz: Relative Frequency Histogram
• Frequency Polygon
• Quiz: Frequency Polygon
• Frequency Distribution
• Stem-and-Leaf
• Box Plot (Box-and-Whiskers)
• Quiz: Box Plot (Box-and-Whiskers)
• Scatter Plot
• Measures of Central Tendency
• Quiz: Measures of Central Tendency
• Measures of Variability
• Quiz: Measures of Variability
• Measurement Scales
• Quiz: Introduction to Numerical Measures
• Classic Theory
• Relative Frequency Theory
• Probability of Simple Events
• Quiz: Probability of Simple Events
• Independent Events
• Dependent Events
• Introduction to Probability
• Quiz: Introduction to Probability
• Probability of Joint Occurrences
• Quiz: Probability of Joint Occurrences
• Non-Mutually-Exclusive Outcomes
• Quiz: Non-Mutually-Exclusive Outcomes
• Double-Counting
• Conditional Probability
• Quiz: Conditional Probability
• Probability Distributions
• Quiz: Probability Distributions
• The Binomial
• Quiz: The Binomial
• Quiz: Sampling Distributions
• Random and Systematic Error
• Central Limit Theorem
• Quiz: Central Limit Theorem
• Populations, Samples, Parameters, and Statistics
• Properties of the Normal Curve
• Quiz: Populations, Samples, Parameters, and Statistics
• Sampling Distributions
• Quiz: Properties of the Normal Curve
• Normal Approximation to the Binomial
• Quiz: Normal Approximation to the Binomial
• Quiz: Stating Hypotheses
• The Test Statistic
• Quiz: The Test Statistic
• Quiz: One- and Two-Tailed Tests
• Type I and II Errors
• Quiz: Type I and II Errors
• Stating Hypotheses
• Significance
• Quiz: Significance
• Point Estimates and Confidence Intervals
• Quiz: Point Estimates and Confidence Intervals
• Estimating a Difference Score
• Quiz: Estimating a Difference Score
• Univariate Tests: An Overview
• Quiz: Univariate Tests: An Overview
• One-Sample z-test
• Quiz: One-Sample z-test
• One-Sample t-test
• Quiz: One-Sample t-test
• Two-Sample z-test for Comparing Two Means
• Quiz: Introduction to Univariate Inferential Tests
• Quiz: Two-Sample z-test for Comparing Two Means
• Two Sample t test for Comparing Two Means
• Quiz: Two-Sample t-test for Comparing Two Means
• Paired Difference t-test
• Quiz: Paired Difference t-test
• Test for a Single Population Proportion
• Quiz: Test for a Single Population Proportion
• Test for Comparing Two Proportions
• Quiz: Test for Comparing Two Proportions
• Quiz: Simple Linear Regression
• Chi-Square (X2)
• Quiz: Chi-Square (X2)
• Correlation
• Quiz: Correlation
• Simple Linear Regression
• Common Mistakes
• Statistics Tables
• Quiz: Cumulative Review A
• Quiz: Cumulative Review B
• Statistics Quizzes

In the previous example, you tested a research hypothesis that predicted not only that the sample mean would be different from the population mean but that it would be different in a specific direction—it would be lower. This test is called a directional or one‐tailed test because the region of rejection is entirely within one tail of the distribution.

Some hypotheses predict only that one value will be different from another, without additionally predicting which will be higher. The test of such a hypothesis is nondirectional or two‐tailed because an extreme test statistic in either tail of the distribution (positive or negative) will lead to the rejection of the null hypothesis of no difference.

Suppose that you suspect that a particular class's performance on a proficiency test is not representative of those people who have taken the test. The national mean score on the test is 74.

The research hypothesis is:

The mean score of the class on the test is not 74.

Or in notation: H a : μ ≠ 74

The null hypothesis is:

The mean score of the class on the test is 74.

In notation: H 0 : μ = 74

As in the last example, you decide to use a 5 percent probability level for the test. Both tests have a region of rejection, then, of 5 percent, or 0.05. In this example, however, the rejection region must be split between both tails of the distribution—0.025 in the upper tail and 0.025 in the lower tail—because your hypothesis specifies only a difference, not a direction, as shown in Figure 1(a). You will reject the null hypotheses of no difference if the class sample mean is either much higher or much lower than the population mean of 74. In the previous example, only a sample mean much lower than the population mean would have led to the rejection of the null hypothesis.

Figure 1.Comparison of (a) a two‐tailed test and (b) a one‐tailed test, at the same probability level (95 percent).

The decision of whether to use a one‐ or a two‐tailed test is important because a test statistic that falls in the region of rejection in a one‐tailed test may not do so in a two‐tailed test, even though both tests use the same probability level. Suppose the class sample mean in your example was 77, and its corresponding z ‐score was computed to be 1.80. Table 2 in "Statistics Tables" shows the critical z ‐scores for a probability of 0.025 in either tail to be –1.96 and 1.96. In order to reject the null hypothesis, the test statistic must be either smaller than –1.96 or greater than 1.96. It is not, so you cannot reject the null hypothesis. Refer to Figure 1(a).

Suppose, however, you had a reason to expect that the class would perform better on the proficiency test than the population, and you did a one‐tailed test instead. For this test, the rejection region of 0.05 would be entirely within the upper tail. The critical z ‐value for a probability of 0.05 in the upper tail is 1.65. (Remember that Table 2 in "Statistics Tables" gives areas of the curve below z ; so you look up the z ‐value for a probability of 0.95.) Your computed test statistic of z = 1.80 exceeds the critical value and falls in the region of rejection, so you reject the null hypothesis and say that your suspicion that the class was better than the population was supported. See Figure 1(b).

In practice, you should use a one‐tailed test only when you have good reason to expect that the difference will be in a particular direction. A two‐tailed test is more conservative than a one‐tailed test because a two‐tailed test takes a more extreme test statistic to reject the null hypothesis.

Previous Quiz: The Test Statistic

Next Quiz: One- and Two-Tailed Tests

• Online Quizzes for CliffsNotes Statistics QuickReview, 2nd Edition

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

11.4: One- and Two-Tailed Tests

• Last updated
• Save as PDF
• Page ID 2148

• Rice University

Learning Objectives

• Define Type I and Type II errors
• Interpret significant and non-significant differences
• Explain why the null hypothesis should not be accepted when the effect is not significant

In the James Bond case study, Mr. Bond was given \(16\) trials on which he judged whether a martini had been shaken or stirred. He was correct on \(13\) of the trials. From the binomial distribution, we know that the probability of being correct \(13\) or more times out of \(16\) if one is only guessing is \(0.0106\). Figure \(\PageIndex{1}\) shows a graph of the binomial distribution. The red bars show the values greater than or equal to \(13\). As you can see in the figure, the probabilities are calculated for the upper tail of the distribution. A probability calculated in only one tail of the distribution is called a "one-tailed probability."

Binomial Calculator

A slightly different question can be asked of the data: "What is the probability of getting a result as extreme or more extreme than the one observed?" Since the chance expectation is \(8/16\), a result of \(3/16\) is equally as extreme as \(13/16\). Thus, to calculate this probability, we would consider both tails of the distribution. Since the binomial distribution is symmetric when \(\pi =0.5\), this probability is exactly double the probability of \(0.0106\) computed previously. Therefore, \(p = 0.0212\). A probability calculated in both tails of a distribution is called a "two-tailed probability" (see Figure \(\PageIndex{2}\)).

Should the one-tailed or the two-tailed probability be used to assess Mr. Bond's performance? That depends on the way the question is posed. If we are asking whether Mr. Bond can tell the difference between shaken or stirred martinis, then we would conclude he could if he performed either much better than chance or much worse than chance. If he performed much worse than chance, we would conclude that he can tell the difference, but he does not know which is which. Therefore, since we are going to reject the null hypothesis if Mr. Bond does either very well or very poorly, we will use a two-tailed probability.

On the other hand, if our question is whether Mr. Bond is better than chance at determining whether a martini is shaken or stirred, we would use a one-tailed probability. What would the one-tailed probability be if Mr. Bond were correct on only \(3\) of the \(16\) trials? Since the one-tailed probability is the probability of the right-hand tail, it would be the probability of getting \(3\) or more correct out of \(16\). This is a very high probability and the null hypothesis would not be rejected.

The null hypothesis for the two-tailed test is \(\pi =0.5\). By contrast, the null hypothesis for the one-tailed test is \(\pi \leq 0.5\). Accordingly, we reject the two-tailed hypothesis if the sample proportion deviates greatly from \(0.5\) in either direction. The one-tailed hypothesis is rejected only if the sample proportion is much greater than \(0.5\). The alternative hypothesis in the two-tailed test is \(\pi \neq 0.5\). In the one-tailed test it is \(\pi > 0.5\).

You should always decide whether you are going to use a one-tailed or a two-tailed probability before looking at the data. Statistical tests that compute one-tailed probabilities are called one-tailed tests; those that compute two-tailed probabilities are called two-tailed tests. Two-tailed tests are much more common than one-tailed tests in scientific research because an outcome signifying that something other than chance is operating is usually worth noting. One-tailed tests are appropriate when it is not important to distinguish between no effect and an effect in the unexpected direction. For example, consider an experiment designed to test the efficacy of a treatment for the common cold. The researcher would only be interested in whether the treatment was better than a placebo control. It would not be worth distinguishing between the case in which the treatment was worse than a placebo and the case in which it was the same because in both cases the drug would be worthless.

Some have argued that a one-tailed test is justified whenever the researcher predicts the direction of an effect. The problem with this argument is that if the effect comes out strongly in the non-predicted direction, the researcher is not justified in concluding that the effect is not zero. Since this is unrealistic, one-tailed tests are usually viewed skeptically if justified on this basis alone.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base

Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

Prevent plagiarism. Run a free check.

For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

Here's why students love Scribbr's proofreading services

Discover proofreading & editing

The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

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.

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).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Bevans, R. (2023, June 22). Hypothesis Testing | A Step-by-Step Guide with Easy Examples. Scribbr. Retrieved April 10, 2024, from https://www.scribbr.com/statistics/hypothesis-testing/

Is this article helpful?

Rebecca Bevans

Other students also liked, choosing the right statistical test | types & examples, understanding p values | definition and examples, what is your plagiarism score.

• The Open University
• Guest user / Sign out
• Study with The Open University

My OpenLearn Profile

Personalise your OpenLearn profile, save your favourite content and get recognition for your learning

About this free course

Become an ou student, download this course, share this free course.

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

4 One-tailed vs two-tailed test

To gain a deeper understanding of how to conduct a hypothesis test, this section will delve into the concepts of one-tailed and two-tailed tests. These tests are vital tools in statistical hypothesis testing, and the decision of which test to employ depends on the research question and hypothesis under examination. It is crucial to give careful thought to the suitable type of test to ensure that the hypothesis is thoroughly tested and precise conclusions are derived from the data. This section will elaborate on this topic in greater detail.

To commence, complete the following activity pertaining to the formulation of null and alternative hypotheses. This exercise may be somewhat challenging, but it serves as an excellent introduction to upcoming discussions – don’t be concerned if you find it difficult!

Activity 3 Hypotheses setting

Read the following statements and then develop a null hypothesis and an alternative hypothesis.

‘It is believed that OU students need to set aside no longer than, on average, 15 hours to study an entire session of an OU course. However, a researcher believes that OU students spend longer studying an entire session of an OU course.’

H 0 : OU students spend, on average, no more than 15 hours studying an entire session of OU course.

H a : OU students spend, on average, more than 15 hours studying an entire session of OU course.

They can also be written as:

H 0 : µ ≤ 15 hours studies

H a : µ > 15 hours studies

µ is a symbol for a population mean. Remember, H 0 and H a are always opposites.

Did you identify any differences between the hypotheses you developed in Activity 1 and Activity 3? The set of hypotheses in Activity 1 has an equal (=) or not equal (≠) supposition (sign) in the statement. However, in Activity 3, the set of hypotheses has less than or equal to (≤) and greater than (>) supposition (sign) in the statement. This creates different conditions that lead to acceptance or rejection of the null hypothesis.

Statistics Resources

• Excel - Tutorials
• Basic Probability Rules
• Single Event Probability
• Complement Rule
• Levels of Measurement
• Independent and Dependent Variables
• Entering Data
• Central Tendency
• Data and Tests
• Displaying Data
• Discussing Statistics In-text
• SEM and Confidence Intervals
• Two-Way Frequency Tables
• Empirical Rule
• Finding Probability
• Accessing SPSS
• Chart and Graphs
• Frequency Table and Distribution
• Descriptive Statistics
• Converting Raw Scores to Z-Scores
• Converting Z-scores to t-scores
• Split File/Split Output
• Partial Eta Squared
• Downloading and Installing G*Power: Windows/PC
• Correlation
• Testing Parametric Assumptions
• One-Way ANOVA
• Two-Way ANOVA
• Repeated Measures ANOVA
• Goodness-of-Fit
• Test of Association
• Pearson's r
• Point Biserial
• Mediation and Moderation
• Simple Linear Regression
• Multiple Linear Regression
• Binomial Logistic Regression
• Multinomial Logistic Regression
• Independent Samples T-test
• Dependent Samples T-test
• Testing Assumptions
• T-tests using SPSS
• T-Test Practice
• Predictive Analytics This link opens in a new window
• Quantitative Research Questions
• Null & Alternative Hypotheses
• One-Tail vs. Two-Tail
• Alpha & Beta
• Associated Probability
• Decision Rule
• Statement of Conclusion
• Statistics Group Sessions

One-Tail vs Two-Tail Tests

Two-tailed Test

When testing a hypothesis, you must determine if it is a one-tailed or a two-tailed test. The most common format is a two-tailed test, meaning the critical region is located in both tails of the distribution. This is also referred to as a non-directional hypothesis.

This type of test is associated with a "neutral" alternative hypothesis. Here are some examples:

• There is a difference between the scores.
• The groups are not equal .
• There is a relationship between the variables.

One-tailed Test

The alternative option is a one-tailed test. As the name implies, the critical region lies in only one tail of the distribution. This is also called a directional  hypothesis. The image below shows a right-tailed test. A left-tailed test would be another type of one-tailed test.

This type of test is associated with a more specific alternative claim. Here are some examples:

• One group is higher than the other.
• There is a decrease in performance.
• Group A performs worse than Group B.
• << Previous: Null & Alternative Hypotheses
• Next: Alpha & Beta >>
• Last Updated: Apr 2, 2024 6:35 PM
• URL: https://resources.nu.edu/statsresources

• Key Differences

Know the Differences & Comparisons

Difference Between One-tailed and Two-tailed Test

To test the hypothesis, test statistics is required, which follows a known distribution. In a test, there are two divisions of probability density curve, i.e. region of acceptance and region of rejection. the region of rejection is called as a critical region .

In the field of research and experiments, it pays to know the difference between one-tailed and two-tailed test, as they are quite commonly used in the process.

Content: One-tailed Test Vs Two-tailed Test

Comparison chart, definition of one-tailed test.

One-tailed test alludes to the significance test in which the region of rejection appears on one end of the sampling distribution. It represents that the estimated test parameter is greater or less than the critical value. When the sample tested falls in the region of rejection, i.e. either left or right side, as the case may be, it leads to the acceptance of alternative hypothesis rather than the null hypothesis. It is primarily applied in chi-square distribution; that ascertains the goodness of fit.

In this statistical hypothesis test, all the critical region, related to α , is placed in any one of the two tails. One-tailed test can be:

• Left-tailed test : When the population parameter is believed to be lower than the assumed one, the hypothesis test carried out is the left-tailed test.
• Right-tailed test : When the population parameter is supposed to be greater than the assumed one, the statistical test conducted is a right-tailed test.

Definition of Two-tailed Test

The two-tailed test is described as a hypothesis test, in which the region of rejection or say the critical area is on both the ends of the normal distribution. It determines whether the sample tested falls within or outside a certain range of values. Therefore, an alternative hypothesis is accepted in place of the null hypothesis, if the calculated value falls in either of the two tails of the probability distribution.

In this test, α is bifurcated into two equal parts, placing half on each side, i.e. it considers the possibility of both positive and negative effects. It is performed to see, whether the estimated parameter is either above or below the assumed parameter, so the extreme values, work as evidence against the null hypothesis.

Key Differences Between One-tailed and Two-tailed Test

The fundamental differences between one-tailed and two-tailed test, is explained below in points:

• One-tailed test, as the name suggest is the statistical hypothesis test, in which the alternative hypothesis has a single end. On the other hand, two-tailed test implies the hypothesis test; wherein the alternative hypothesis has dual ends.
• In the one-tailed test, the alternative hypothesis is represented directionally. Conversely, the two-tailed test is a non-directional hypothesis test.
• In a one-tailed test, the region of rejection is either on the left or right of the sampling distribution. On the contrary, the region of rejection is on both the sides of the sampling distribution.
• A one-tailed test is used to ascertain if there is any relationship between variables in a single direction, i.e. left or right. As against this, the two-tailed test is used to identify whether or not there is any relationship between variables in either direction.
• In a one-tailed test, the test parameter calculated is more or less than the critical value. Unlike, two-tailed test, the result obtained is within or outside critical value.
• When an alternative hypothesis has ‘≠’ sign, then a two-tailed test is performed. In contrast, when an alternative hypothesis has ‘> or <‘ sign, then one-tailed test is carried out.

To sum up, we can say that the basic difference between one-tailed and two-tailed test lies in the direction, i.e. in case the research hypothesis entails the direction of interrelation or difference, then one-tailed test is applied, but if the research hypothesis does not signify the direction of interaction or difference, we use two-tailed test.

You Might Also Like:

Swati Aggarwal says

April 24, 2018 at 11:47 am

Very Informative and specifically summarised. thank you.

Aurobindo says

January 20, 2019 at 8:22 am

Amazing Surbhi. I recently started following this site and I really find it very very useful. The simplicity of language, the key distinctions, range of depth covered in giving the differences. Hats off to you for your effort. Very amazing. I have definitely bookmarked this website as ‘my favorite’ and I shall keep visiting it again and again. Keep it up. Thanks.

Marian Truehill says

July 23, 2020 at 11:48 pm

This website is very useful and easy to understand for Statistics methods and concepts.

Kuje Samson says

January 11, 2023 at 5:13 am

The website is very linear to a layman statistics. I really enjoyed visiting the site

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Search Search Please fill out this field.

What Is a Two-Tailed Test?

Understanding a two-tailed test, special considerations, two-tailed vs. one-tailed test.

• Two-Tailed Test FAQs
• Corporate Finance
• Financial Analysis

What Is a Two-Tailed Test? Definition and Example

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

Investopedia / Joules Garcia

A two-tailed test, in statistics, is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. It is used in null-hypothesis testing and testing for statistical significance . If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.

Key Takeaways

• In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values.
• It is used in null-hypothesis testing and testing for statistical significance.
• If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.
• By convention two-tailed tests are used to determine significance at the 5% level, meaning each side of the distribution is cut at 2.5%.

A basic concept of inferential statistics is hypothesis testing , which determines whether a claim is true or not given a population parameter. A hypothesis test that is designed to show whether the mean of a sample is significantly greater than and significantly less than the mean of a population is referred to as a two-tailed test. The two-tailed test gets its name from testing the area under both tails of a normal distribution , although the test can be used in other non-normal distributions.

A two-tailed test is designed to examine both sides of a specified data range as designated by the probability distribution involved. The probability distribution should represent the likelihood of a specified outcome based on predetermined standards. This requires the setting of a limit designating the highest (or upper) and lowest (or lower) accepted variable values included within the range. Any data point that exists above the upper limit or below the lower limit is considered out of the acceptance range and in an area referred to as the rejection range.

There is no inherent standard about the number of data points that must exist within the acceptance range. In instances where precision is required, such as in the creation of pharmaceutical drugs, a rejection rate of 0.001% or less may be instituted. In instances where precision is less critical, such as the number of food items in a product bag, a rejection rate of 5% may be appropriate.

A two-tailed test can also be used practically during certain production activities in a firm, such as with the production and packaging of candy at a particular facility. If the production facility designates 50 candies per bag as its goal, with an acceptable distribution of 45 to 55 candies, any bag found with an amount below 45 or above 55 is considered within the rejection range.

To confirm the packaging mechanisms are properly calibrated to meet the expected output, random sampling may be taken to confirm accuracy. A simple random sample takes a small, random portion of the entire population to represent the entire data set, where each member has an equal probability of being chosen.

For the packaging mechanisms to be considered accurate, an average of 50 candies per bag with an appropriate distribution is desired. Additionally, the number of bags that fall within the rejection range needs to fall within the probability distribution limit considered acceptable as an error rate. Here, the null hypothesis would be that the mean is 50 while the alternate hypothesis would be that it is not 50.

If, after conducting the two-tailed test, the z-score falls in the rejection region, meaning that the deviation is too far from the desired mean, then adjustments to the facility or associated equipment may be required to correct the error. Regular use of two-tailed testing methods can help ensure production stays within limits over the long term.

Be careful to note if a statistical test is one- or two-tailed as this will greatly influence a model's interpretation.

When a hypothesis test is set up to show that the sample mean would be only higher than the population mean, this is referred to as a  one-tailed test . A formulation of this hypothesis would be, for example, that "the returns on an investment fund would be  at least  x%." One-tailed tests could also be set up to show that the sample mean could be only less than the population mean. The key difference from a two-tailed test is that in a two-tailed test, the sample mean could be different from the population mean by being  either  higher or lower than it.

If the sample being tested falls into the one-sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis. A one-tailed test is also known as a directional hypothesis or directional test.

A two-tailed test, on the other hand, is designed to examine both sides of a specified data range to test whether a sample is greater than or less than the range of values.

Example of a Two-Tailed Test

As a hypothetical example, imagine that a new  stockbroker , named XYZ, claims that their brokerage fees are lower than that of your current stockbroker, ABC) Data available from an independent research firm indicates that the mean and standard deviation of all ABC broker clients are $18 and $6, respectively.

A sample of 100 clients of ABC is taken, and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and the sample standard deviation is $6, can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?

• H 0 : Null Hypothesis: mean = 18
• H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)
• Rejection region: Z <= - Z 2.5  and Z>=Z 2.5  (assuming 5% significance level, split 2.5 each on either side).
• Z = (sample mean – mean) / (std-dev / sqrt (no. of samples)) = (18.75 – 18) / (6/(sqrt(100)) = 1.25

This calculated Z value falls between the two limits defined by: - Z 2.5  = -1.96 and Z 2.5  = 1.96.

This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker. Therefore, the null hypothesis cannot be rejected. Alternatively, the p-value = P(Z< -1.25)+P(Z >1.25) = 2 * 0.1056 = 0.2112 = 21.12%, which is greater than 0.05 or 5%, leads to the same conclusion.

How Is a Two-Tailed Test Designed?

A two-tailed test is designed to determine whether a claim is true or not given a population parameter. It examines both sides of a specified data range as designated by the probability distribution involved. As such, the probability distribution should represent the likelihood of a specified outcome based on predetermined standards.

What Is the Difference Between a Two-Tailed and One-Tailed Test?

A two-tailed hypothesis test is designed to show whether the sample mean is significantly greater than  or  significantly less than the mean of a population. The two-tailed test gets its name from testing the area under both tails (sides) of a normal distribution. A one-tailed hypothesis test, on the other hand, is set up to show only one test; that the sample mean would be higher than the population mean, or, in a separate test, that the sample mean would be lower than the population mean.

What Is a Z-score?

A Z-score numerically describes a value's relationship to the mean of a group of values and is measured in terms of the number of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score whereas Z-scores of 1.0 and -1.0 would indicate values one standard deviation above or below the mean. In most large data sets, 99% of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above and below the mean.

San Jose State University. " 6: Introduction to Null Hypothesis Significance Testing ."

• Terms of Service
• Editorial Policy
• Privacy Policy
• Your Privacy Choices

Statistics Made Easy

One-Tailed Hypothesis Tests: 3 Example Problems

In statistics, we use hypothesis tests to determine whether some claim about a population parameter is true or not.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter = ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter <, >, ≠ some value

There are two types of hypothesis tests:

• Two-tailed test : Alternative hypothesis contains the ≠ sign
• One-tailed test : Alternative hypothesis contains either < or > sign

In a one-tailed test , the alternative hypothesis contains the less than (“<“) or greater than (“>”) sign. This indicates that we’re testing whether or not there is a positive or negative effect.

Check out the following example problems to gain a better understanding of one-tailed tests.

Example 1: Factory Widgets

Suppose it’s assumed that the average weight of a certain widget produced at a factory is 20 grams. However, one engineer believes that a new method produces widgets that weigh less than 20 grams.

To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses:

• H 0 (Null Hypothesis): μ ≥ 20 grams
• H A (Alternative Hypothesis): μ < 20 grams

Note : We can tell this is a one-tailed test because the alternative hypothesis contains the less than ( < ) sign. Specifically, we would call this a left-tailed test because we’re testing if some population parameter is less than a specific value.

To test this, he uses the new method to produce 20 widgets and obtains the following information:

• n = 20 widgets
• x = 19.8 grams
• s = 3.1 grams

Plugging these values into the One Sample t-test Calculator , we obtain the following results:

• t-test statistic: -0.288525
• one-tailed p-value: 0.388

Since the p-value is not less than .05, the engineer fails to reject the null hypothesis.

He does not have sufficient evidence to say that the true mean weight of widgets produced by the new method is less than 20 grams.

Example 2: Plant Growth

Suppose a standard fertilizer has been shown to cause a species of plants to grow by an average of 10 inches. However, one botanist believes a new fertilizer can cause this species of plants to grow by an average of greater than 10 inches.

To test this, she can perform a one-tailed hypothesis test with the following null and alternative hypotheses:

• H 0 (Null Hypothesis): μ ≤ 10 inches
• H A (Alternative Hypothesis): μ > 10 inches

Note : We can tell this is a one-tailed test because the alternative hypothesis contains the greater than ( > ) sign. Specifically, we would call this a right-tailed test because we’re testing if some population parameter is greater than a specific value.

To test this claim, she applies the new fertilizer to a simple random sample of 15 plants and obtains the following information:

• n = 15 plants
• x = 11.4 inches
• s = 2.5 inches
• t-test statistic: 2.1689
• one-tailed p-value: 0.0239

Since the p-value is less than .05, the botanist rejects the null hypothesis.

She has sufficient evidence to conclude that the new fertilizer causes an average increase of greater than 10 inches.

Example 3: Studying Method

A professor currently teaches students to use a studying method that results in an average exam score of 82. However, he believes a new studying method can produce exam scores with an average value greater than 82.

To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses:

• H 0 (Null Hypothesis): μ ≤ 82
• H A (Alternative Hypothesis): μ > 82

To test this claim, the professor has 25 students use the new studying method and then take the exam. He collects the following data on the exam scores for this sample of students:

• t-test statistic: 3.6586
• one-tailed p-value: 0.0006

Since the p-value is less than .05, the professor rejects the null hypothesis.

He has sufficient evidence to conclude that the new studying method produces exam scores with an average score greater than 82.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing What is a Directional Hypothesis? When Do You Reject the Null Hypothesis?

Published by Zach

Leave a reply cancel reply.

Your email address will not be published. Required fields are marked *

• Statistics with Python
• Data Analysis Tutorial
• Python – Data visualization tutorial
• Machine Learning Projects
• Machine Learning Interview Questions
• Machine Learning Mathematics
• Deep Learning Tutorial
• Deep Learning Project
• Deep Learning Interview Questions
• Computer Vision Tutorial
• Computer Vision Projects
• NLP Project
• NLP Interview Questions
• 100 Days of Machine Learning
• Difference Between Business Analytics and Predictive Analytics
• Difference between Google Jamboard and Microsoft Whiteboard
• Difference Between GAGAN and GPS
• Difference Between Latency and Throughput
• Difference Between Google Analytics and Piwik
• Difference Between Google and Wikipedia
• Difference between scaling horizontally and vertically for databases
• Flutter vs Flutter 2
• Difference between Paper and Article for Scientific Writings
• Difference between CIFS vs SMB
• Differences between Software Testing and Quality Assurance
• Difference between Website and Blog
• Difference Between DOS and Windows
• Bitcoin vs Litecoin - What's the Difference?
• Differences between Low-Code and No-Code Development
• Difference Between VLAN and VPN
• Difference Between Cloudflare and CloudFront
• Differences between System Analysis and System Design
• Difference between Research Papers and Technical Articles for Journal Publication

Difference Between One-Tailed and Two-Tailed Tests

One and Two-Tailed Tests are ways to identify the relationship between the statistical variables. For checking the relationship between variables in a single direction (Left or Right direction), we use a one-tailed test. A two-tailed test is used to check whether the relations between variables are in any direction or not.

One-Tailed Test

A one-tailed test is based on a uni-directional hypothesis where the area of rejection is on only one side of the sampling distribution. It determines whether a particular population parameter is larger or smaller than the predefined parameter. It uses one single critical value to test the data.

Alternative Hypothesis ( H 1​):

Test Statistic: Depending on the type of test and the distribution, the test statistic is computed ( Z -score for normal distribution).

Decision Rule: If the test statistic falls in the critical region, reject the null hypothesis in favor of the alternative hypothesis.

Example: Effect of participants of students in coding competition on their fear level.

• H0: There is no important effect of students in coding competition on their fear level. 

The main intention is to check the decreased fear level when students participate in a coding competition.

Two-Tailed Test

A two-tailed test is also called a nondirectional hypothesis. For checking whether the sample is greater or less than a range of values, we use the two-tailed. It is used for null hypothesis testing.

Test Statistic: Compute the test statistic as appropriate for the distribution ( Z -score for normal distribution).

Decision Rule: If the test statistic falls in either tail of the distribution’s critical region, reject the null hypothesis in favor of the alternative hypothesis.

Example: Effect of new bill pass on the loan of farmers. 

• H0: There is no significant effect of the new bill passed on loans of farmers.

New bill passes can affect in both ways either increase or decrease the loan of farmers.

Difference Between One and Two-Tailed Test:

Please Login to comment...

Similar reads.

• ML-Statistics
• Difference Between
• How to Use ChatGPT with Bing for Free?
• 7 Best Movavi Video Editor Alternatives in 2024
• How to Edit Comment on Instagram
• 10 Best AI Grammar Checkers and Rewording Tools
• 30 OOPs Interview Questions and Answers (2024)

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

We've detected unusual activity from your computer network

To continue, please click the box below to let us know you're not a robot.

Why did this happen?

Please make sure your browser supports JavaScript and cookies and that you are not blocking them from loading. For more information you can review our Terms of Service and Cookie Policy .

For inquiries related to this message please contact our support team and provide the reference ID below.