meaning of quantitative analysis in education

How To Use Quantitative Data in Education

Quantitative data in education has increasingly valuable, providing educators with valuable insights into student performance and informing data-driven decision-making. In this article, we’ll explore the various aspects of using quantitative data in education, from understanding its definition and importance to analyzing and applying it effectively. We will also discuss the challenges that educators may encounter and the solutions to overcome them.

Let’s dive in!

• Understanding Quantitative Data
• Types of Quantitative Data in Education
• Gathering Quantitative Data in Education
• Ethical Considerations in Data Collection
• Analyzing Quantitative Data
• Applying Quantitative Data in Education
• Challenges and Solutions in Using Quantitative Data

1.  Understanding Quantitative Data

Before delving into the world of quantitative data, it’s important to have a clear understanding of what it entails and why it is essential in education. Quantitative data refers to numerical information that can be measured and analyzed statistically. It provides educators with objective measurements that help identify patterns, trends, and correlations in student performance.

Quantitative data plays a crucial role in education as it allows educators to make data-driven decisions. By collecting and analyzing these data points, educators can gain valuable insights into student achievement, identify areas for improvement, and make informed decisions to enhance teaching and learning.

Moreover, quantitative data allows educators to track progress over time, evaluate the effectiveness of interventions and instructional strategies, and compare student performance across different groups or demographics. It provides a solid foundation for evidence-based decision-making in education. To learn more, check out our blog post rounding up quantitive data examples in education .

2.  Types of Quantitative Data in Education

There are different types of quantitative data that educators can collect in the field of education. These include achievement data, demographic data, and behavioral data.

Achievement data, such as test scores and grades, provide insights into student performance and growth. These data points can help educators assess the effectiveness of their instructional methods and identify areas where students may need additional support.

Demographic data, on the other hand, offers information about student characteristics like gender, ethnicity, and socioeconomic status. This data can help educators understand the diverse backgrounds and experiences of their students, which in turn can inform instructional practices and create a more inclusive learning environment.

Lastly, behavioral data, such as attendance and disciplinary records, shed light on student engagement and behavior patterns. By analyzing this data, educators can identify students who may be at risk of falling behind or exhibiting problematic behavior. This allows for early intervention and support to be provided, ensuring that all students have the opportunity to succeed.

Read next: A guide to the different types of data in education (and which ones to collect)

3.  Gathering Quantitative Data in Education

Collecting quantitative data requires the use of appropriate tools and methodologies. Educators can leverage various data collection methods, such as surveys, assessments, and direct observations, to gather the necessary information.

When it comes to gathering quantitative data in education, educators have a wide range of tools at their disposal. These tools not only make the data collection process more efficient but also provide valuable insights into student performance and learning outcomes.

Tools for Collecting Quantitative Data

In the digital age, technology plays a crucial role in data collection. Educators can utilize online surveys and assessment platforms to gather quantitative data efficiently. These tools not only streamline the data collection process but also provide instant results and data visualization capabilities, enabling educators to analyze and interpret the data more effectively.

For example, online survey platforms allow educators to design and distribute surveys to gather information about student demographics, attitudes, and preferences. These surveys can be customized to collect quantitative data, such as Likert scale responses or numerical ratings. The data collected from these surveys can provide valuable insights into student experiences and perceptions, helping educators make informed decisions about instructional strategies and curriculum development.

In addition to online surveys, assessments are another valuable tool for collecting quantitative data. Standardized tests and assessments provide consistent and comparable measures of student achievement. By administering these tests, educators can gather objective data that can be used to assess student performance and identify strengths and weaknesses.

Standardized tests, such as state-mandated assessments or national exams, are designed to measure student knowledge and skills in specific subject areas. These tests provide educators with standardized scores that can be used to compare student performance across schools, districts, or even countries. This data can inform educational policies and interventions, helping educators identify areas of improvement and allocate resources effectively.

4.  Ethical Considerations in Data Collection

While collecting quantitative data, it’s essential to prioritize student privacy and confidentiality. Educators must ensure that data collection methods comply with ethical guidelines and regulations. This includes obtaining informed consent from students or their guardians, anonymizing data when necessary, and protecting sensitive information.

Furthermore, educators should be mindful of potential biases in data collection. It’s important to use data collection methods that are fair and unbiased, avoiding any potential discrimination or stigmatization. For example, when designing surveys or assessments, educators should ensure that the questions and tasks are culturally sensitive and inclusive, taking into account the diverse backgrounds and experiences of students.

By upholding ethical standards in data collection, educators can maintain the trust and confidence of students, parents, and the broader educational community. This trust is essential for the successful implementation of data-driven decision-making processes and the improvement of educational outcomes for all students.

5.  Analyzing Quantitative Data

Analyzing quantitative data involves making sense of the collected information to derive meaningful insights and inform decision-making. Educators can leverage various statistical concepts and software tools to analyze quantitative data effectively.

When analyzing quantitative data, educators should consider the context in which the data was collected. Understanding the purpose and objectives of the data collection process helps in selecting appropriate statistical techniques and interpreting the results accurately. Additionally, educators should ensure that the data is reliable and valid, as this is crucial for drawing accurate conclusions.

Software for Quantitative Data Analysis

There are various software tools available that facilitate the analysis of quantitative data. Spreadsheet applications like Microsoft Excel and Google Sheets offer basic data analysis functionalities, such as sorting, filtering, and creating charts and graphs.

Advanced statistical software packages, such as SPSS and R, provide more powerful capabilities for analyzing quantitative data. These tools enable educators to conduct sophisticated statistical analyses and perform complex calculations. It’s important for educators to familiarize themselves with these software packages to make the most of their quantitative data.

In addition to statistical software, educators can also explore data visualization tools like Inno™ Starter Kits . These plug-and-play templates allow educators to create interactive and visually appealing charts, graphs, and dashboards, making it easier to communicate findings and insights to stakeholders.

6.  Applying Quantitative Data in Education

Using quantitative data in education goes beyond mere analysis. It involves applying the insights gained from the data to drive positive change and enhance teaching and learning.

Data-Driven Decision Making in Education

Data-driven decision making involves using quantitative data to inform educational policies, instructional practices, and resource allocation. By analyzing trends and patterns in student performance, educators can identify areas of improvement and develop targeted interventions.

For instance, if the data reveals that a particular group of students is struggling in a specific subject area, educators can design tailored interventions to address their needs. By continuously monitoring the impact of these interventions through data analysis, educators can evaluate their effectiveness and make adjustments as needed.

Enhancing Teaching and Learning through Quantitative Data

Quantitative data can also be used to enhance teaching and learning on an individual level. By analyzing student achievement data, educators can identify gaps in knowledge and tailor instruction accordingly.

Additionally, quantitative data can be used to track student progress over time, allowing educators to celebrate growth and provide targeted feedback. It empowers educators to identify areas for improvement and implement evidence-based instructional strategies that maximize student learning outcomes.

7.  Challenges and Solutions in Using Quantitative Data

While leveraging quantitative data in education has immense benefits, educators may encounter challenges along the way. It’s essential to be aware of these obstacles and develop effective strategies to overcome them.

Common Obstacles in Data Utilization

One common challenge is the lack of data literacy among educators. Without a solid understanding of data analysis concepts and techniques, educators may struggle to effectively interpret and utilize quantitative data. Addressing this challenge requires providing professional development opportunities and building educators’ capacity in data analysis.

Furthermore, logistical challenges, such as data quality and data integration across different systems, can hinder effective data utilization. Educators must ensure that data collection methods are rigorous and reliable, and data systems are interoperable to consolidate information effectively.

Overcoming Challenges in Data Analysis and Application

To overcome these challenges, educators can collaborate with data specialists or engage in professional learning communities to enhance their data analysis skills. Additionally, establishing a culture of data sharing and collaboration within schools or districts can foster a supportive environment for effective data utilization.

Moreover, providing educators with tools and resources that simplify data analysis and visualization can streamline the process and make it more accessible to a wider range of educators.

Read next: How data analytics is reshaping the education industry

Key takeaways

Using quantitative data is a powerful tool in education, allowing educators to make evidence-based decisions, identify areas for improvement, and enhance teaching and learning. By understanding the definition and importance of quantitative data, gathering it effectively, analyzing it using appropriate tools and methodologies, and applying the insights gained, educators can unlock the full potential of quantitative data to drive positive change in education.

Diving deep into quantitative data is essential for progressive education, but the challenge often lies in visualizing and interpreting that data effectively. If you’re eager to simplify this process and present your findings more dynamically, we encourage you to explore our Inno™ Starter Kits . Tailored for educators, these kits offer a streamlined approach to viewing and understanding quantitative student data, helping you make informed decisions with confidence. Turn data into actionable insights and take your educational strategies to the next level!

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Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative research is a systematic investigation that primarily focuses on quantifying data, variables, and relationships. It involves the use of statistical, mathematical, and computational techniques to collect and analyze data. Quantitative research is often used to establish patterns, test hypotheses, and make predictions. It is widely applied in fields such as psychology, sociology, economics, health sciences, and education.

Quantitative Research

Quantitative research is a research approach that seeks to quantify data and generalize results from a sample to a larger population. It relies on structured data collection methods and employs statistical analysis to interpret results. This type of research is objective, and findings are typically presented in numerical form, allowing for comparison and generalization.

Key Characteristics of Quantitative Research :

• Objective : Focuses on numbers and measurable variables rather than subjective opinions.
• Structured : Employs well-defined research questions, hypotheses, and data collection methods.
• Statistical : Utilizes statistical tools to analyze data and validate findings.
• Replicable : Enables repetition of the study to verify results and increase reliability.

Example : A survey on the correlation between exercise frequency and stress levels among adults, using a Likert scale to measure responses.

Types of Quantitative Research

Quantitative research can be categorized into several types, each serving a specific purpose. The most common types include descriptive , correlational , experimental , and causal-comparative research.

1. Descriptive Research

Definition : Descriptive research describes characteristics or behaviors of a population without examining relationships or causes. It provides a snapshot of current conditions or attitudes.

Purpose : To gather information and create an overview of a particular phenomenon, population, or condition.

Example : A survey describing the demographics and academic performance of students at a university.

2. Correlational Research

Definition : Correlational research examines the relationship between two or more variables but does not imply causation. It analyzes patterns to determine if variables are associated or occur together.

Purpose : To identify associations or trends among variables without establishing cause and effect.

Example : Investigating the relationship between social media use and self-esteem among teenagers.

3. Experimental Research

Definition : Experimental research manipulates one or more independent variables to observe the effect on a dependent variable, establishing cause-and-effect relationships. This type of research involves control and experimental groups.

Purpose : To test hypotheses by isolating and controlling variables to establish causality.

Example : Testing the effect of a new medication on blood pressure by administering it to one group (experimental) and comparing it to a placebo group (control).

4. Causal-Comparative (Ex Post Facto) Research

Definition : Causal-comparative research investigates the cause-effect relationship between variables when experimental manipulation is not possible. It compares groups that differ on a particular variable to determine the effect of that variable.

Purpose : To explore cause-and-effect relationships retrospectively by comparing pre-existing groups.

Example : Studying the impact of different teaching methods on student performance by comparing classes taught with traditional versus technology-assisted instruction.

Quantitative Research Methods

Quantitative research methods focus on systematic data collection and analysis using structured techniques. Common methods include surveys , experiments , and observations .

Definition : Surveys are a popular quantitative method that involves asking participants standardized questions to collect data on their opinions, behaviors, or demographics. Surveys can be conducted via questionnaires, interviews, or online forms.

Purpose : To gather data from a large sample, allowing researchers to make inferences about the larger population.

Example : Conducting a survey to collect customer satisfaction data from a random sample of customers in a retail store.

Advantages :

• Cost-effective and time-efficient for large sample sizes.
• Provides structured data that is easy to analyze statistically.

Disadvantages :

• Limited depth, as responses are often restricted to specific options.
• Potential for response bias, where participants may not answer truthfully.

2. Experiments

Definition : Experiments involve manipulating one or more variables in a controlled environment to observe the effect on another variable. Experiments are often conducted in laboratories or controlled settings to maintain precision and limit external influences.

Purpose : To test hypotheses and establish cause-and-effect relationships.

Example : Conducting a laboratory experiment to test the effect of light exposure on sleep patterns.

• High level of control over variables.
• Establishes causality, which can support theory-building.
• Limited external validity, as findings may not always apply outside of the controlled setting.
• Ethical considerations may limit experimentation on certain subjects or groups.

3. Observations

Definition : Observational research involves systematically observing and recording behavior or events as they occur naturally, without interference. While often used in qualitative research, structured observational methods can yield quantitative data.

Purpose : To gather real-world data in a non-intrusive manner.

Example : Observing customer behavior in a store to track time spent in different areas and identify shopping patterns.

• Provides data on actual behaviors rather than self-reported responses.
• Useful for gathering data on situations where surveys or experiments may not be feasible.
• Observer bias may affect results.
• Can be time-consuming, especially if behaviors are infrequent or complex.

Data Collection Tools in Quantitative Research

Quantitative research relies on various tools to collect and quantify data, including:

• Questionnaires : Standardized forms with close-ended questions, often using scales (e.g., Likert scale) for responses.
• Tests and Assessments : Used to measure knowledge, skills, or other measurable attributes.
• Digital Tracking Tools : Software or digital applications that collect data, such as website traffic metrics or physiological monitoring devices.

Data Analysis in Quantitative Research

Data analysis in quantitative research involves statistical techniques to interpret numerical data and determine relationships or trends. Key techniques include descriptive statistics , inferential statistics , and correlation analysis .

1. Descriptive Statistics

Definition : Descriptive statistics summarize and organize data, providing basic information such as mean, median, mode, standard deviation, and range.

Purpose : To give an overview of the dataset, allowing researchers to understand general trends and distributions.

Example : Calculating the average test scores of students in a school to assess overall performance.

Common Measures :

• Mean : Average of all data points.
• Median : Middle value of an ordered dataset.
• Standard Deviation : Measure of variability around the mean.

2. Inferential Statistics

Definition : Inferential statistics allow researchers to make predictions or inferences about a population based on sample data. Techniques include hypothesis testing, t-tests, ANOVA, and regression analysis.

Purpose : To determine if observed results are statistically significant and can be generalized to a larger population.

Example : Using a t-test to compare average scores between two different teaching methods to see if one is significantly more effective.

Common Tests :

• t-Test : Compares the means of two groups to determine if they are statistically different.
• ANOVA (Analysis of Variance) : Compares means among three or more groups.
• Regression Analysis : Examines the relationship between independent and dependent variables.

3. Correlation Analysis

Definition : Correlation analysis measures the strength and direction of the relationship between two variables. It is used to determine if changes in one variable are associated with changes in another.

Purpose : To identify associations between variables without implying causation.

Example : Calculating the correlation coefficient between screen time and academic performance to determine if there is an association.

• Pearson Correlation Coefficient (r) : Measures linear correlation between two continuous variables.
• Spearman’s Rank Correlation : Measures correlation between two ranked variables.

Advantages and Disadvantages of Quantitative Research

• Objective : Minimizes researcher bias by focusing on numerical data.
• Generalizable : Findings from large, random samples can often be applied to a broader population.
• Replicable : Structured methods make it possible for other researchers to replicate studies and verify results.

Disadvantages

• Limited Depth : Quantitative research often lacks the depth of qualitative insights.
• Rigid Structure : Limited flexibility in data collection and analysis.
• Potential Bias : Response or sampling biases can affect results, especially in survey-based studies.

Tips for Conducting Effective Quantitative Research

• Define Clear Objectives : Develop specific research questions or hypotheses to guide the study.
• Choose the Right Method : Select a quantitative method that aligns with the research goals and type of data needed.
• Ensure Sample Representativeness : Use appropriate sampling techniques to ensure results can be generalized.
• Employ Proper Statistical Tools : Choose analysis techniques that match the nature of the data and research questions.
• Interpret Results Accurately : Avoid overgeneralizing findings and consider limitations when interpreting results.

Quantitative research provides a structured, objective approach to investigating research questions, allowing for statistical analysis, pattern recognition, and hypothesis testing. With methods like surveys, experiments, and observational studies, quantitative research offers valuable insights across diverse fields, from social sciences to healthcare. By applying rigorous statistical analysis, researchers can draw meaningful conclusions, contributing to the body of scientific knowledge and helping inform data-driven decisions.

• Creswell, J. W., & Creswell, J. D. (2018). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (5th ed.). SAGE Publications.
• Punch, K. F. (2014). Introduction to Social Research: Quantitative and Qualitative Approaches (3rd ed.). SAGE Publications.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications.
• Trochim, W. M., & Donnelly, J. P. (2008). The Research Methods Knowledge Base (3rd ed.). Cengage Learning.
• Babbie, E. R. (2021). The Practice of Social Research (15th ed.). Cengage Learning.

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Qualitative vs. quantitative data analysis: How do they differ?

Learning analytics have become the cornerstone for personalizing student experiences and enhancing learning outcomes. In this data-informed approach to education there are two distinct methodologies: qualitative and quantitative analytics. These methods, which are typical to data analytics in general, are crucial to the interpretation of learning behaviors and outcomes. This blog will explore the nuances that distinguish qualitative and quantitative research, while uncovering their shared roles in learning analytics, program design and instruction.

What is qualitative data?

Qualitative data is descriptive and includes information that is non numerical. Qualitative research is used to gather in-depth insights that can't be easily measured on a scale like opinions, anecdotes and emotions. In learning analytics qualitative data could include in depth interviews, text responses to a prompt, or a video of a class period. 1

What is quantitative data?

Quantitative data is information that has a numerical value. Quantitative research is conducted to gather measurable data used in statistical analysis. Researchers can use quantitative studies to identify patterns and trends. In learning analytics quantitative data could include test scores, student demographics, or amount of time spent in a lesson. 2

Key difference between qualitative and quantitative data

It's important to understand the differences between qualitative and quantitative data to both determine the appropriate research methods for studies and to gain insights that you can be confident in sharing.

Data Types and Nature

Examples of qualitative data types in learning analytics:

• Observational data of human behavior from classroom settings such as student engagement, teacher-student interactions, and classroom dynamics
• Textual data from open-ended survey responses, reflective journals, and written assignments
• Feedback and discussions from focus groups or interviews
• Content analysis from various media

Examples of quantitative data types:

• Standardized test, assessment, and quiz scores
• Grades and grade point averages
• Attendance records
• Time spent on learning tasks
• Data gathered from learning management systems (LMS), including login frequency, online participation, and completion rates of assignments

Methods of Collection

Qualitative and quantitative research methods for data collection can occasionally seem similar so it's important to note the differences to make sure you're creating a consistent data set and will be able to reliably draw conclusions from your data.

Qualitative research methods

Because of the nature of qualitative data (complex, detailed information), the research methods used to collect it are more involved. Qualitative researchers might do the following to collect data:

• Conduct interviews to learn about subjective experiences
• Host focus groups to gather feedback and personal accounts
• Observe in-person or use audio or video recordings to record nuances of human behavior in a natural setting
• Distribute surveys with open-ended questions

Quantitative research methods

Quantitative data collection methods are more diverse and more likely to be automated because of the objective nature of the data. A quantitative researcher could employ methods such as:

• Surveys with close-ended questions that gather numerical data like birthdates or preferences
• Observational research and record measurable information like the number of students in a classroom
• Automated numerical data collection like information collected on the backend of a computer system like button clicks and page views

Analysis techniques

Qualitative and quantitative data can both be very informative. However, research studies require critical thinking for productive analysis.

Qualitative data analysis methods

Analyzing qualitative data takes a number of steps. When you first get all your data in one place you can do a review and take notes of trends you think you're seeing or your initial reactions. Next, you'll want to organize all the qualitative data you've collected by assigning it categories. Your central research question will guide your data categorization whether it's by date, location, type of collection method (interview vs focus group, etc), the specific question asked or something else. Next, you'll code your data. Whereas categorizing data is focused on the method of collection, coding is the process of identifying and labeling themes within the data collected to get closer to answering your research questions. Finally comes data interpretation. To interpret the data you'll take a look at the information gathered including your coding labels and see what results are occurring frequently or what other conclusions you can make. 3

Quantitative analysis techniques

The process to analyze quantitative data can be time-consuming due to the large volume of data possible to collect. When approaching a quantitative data set, start by focusing in on the purpose of your evaluation. Without making a conclusion, determine how you will use the information gained from analysis; for example: The answers of this survey about study habits will help determine what type of exam review session will be most useful to a class. 4

Next, you need to decide who is analyzing the data and set parameters for analysis. For example, if two different researchers are evaluating survey responses that rank preferences on a scale from 1 to 5, they need to be operating with the same understanding of the rankings. You wouldn't want one researcher to classify the value of 3 to be a positive preference while the other considers it a negative preference. It's also ideal to have some type of data management system to store and organize your data, such as a spreadsheet or database. Within the database, or via an export to data analysis software, the collected data needs to be cleaned of things like responses left blank, duplicate answers from respondents, and questions that are no longer considered relevant. Finally, you can use statistical software to analyze data (or complete a manual analysis) to find patterns and summarize your findings. 4

Qualitative and quantitative research tools

From the nuanced, thematic exploration enabled by tools like NVivo and ATLAS.ti, to the statistical precision of SPSS and R for quantitative analysis, each suite of data analysis tools offers tailored functionalities that cater to the distinct natures of different data types.

Qualitative research software:

NVivo: NVivo is qualitative data analysis software that can do everything from transcribe recordings to create word clouds and evaluate uploads for different sentiments and themes. NVivo is just one tool from the company Lumivero, which offers whole suites of data processing software. 5

ATLAS.ti: Similar to NVivo, ATLAS.ti allows researchers to upload and import data from a variety of sources to be tagged and refined using machine learning and presented with visualizations and ready for insert into reports. 6

SPSS: SPSS is a statistical analysis tool for quantitative research, appreciated for its user-friendly interface and comprehensive statistical tests, which makes it ideal for educators and researchers. With SPSS researchers can manage and analyze large quantitative data sets, use advanced statistical procedures and modeling techniques, predict customer behaviors, forecast market trends and more. 7

R: R is a versatile and dynamic open-source tool for quantitative analysis. With a vast repository of packages tailored to specific statistical methods, researchers can perform anything from basic descriptive statistics to complex predictive modeling. R is especially useful for its ability to handle large datasets, making it ideal for educational institutions that generate substantial amounts of data. The programming language offers flexibility in customizing analysis and creating publication-quality visualizations to effectively communicate results. 8

Applications in Educational Research

Both quantitative and qualitative data can be employed in learning analytics to drive informed decision-making and pedagogical enhancements. In the classroom, quantitative data like standardized test scores and online course analytics create a foundation for assessing and benchmarking student performance and engagement. Qualitative insights gathered from surveys, focus group discussions, and reflective student journals offer a more nuanced understanding of learners' experiences and contextual factors influencing their education. Additionally feedback and practical engagement metrics blend these data types, providing a holistic view that informs curriculum development, instructional strategies, and personalized learning pathways. Through these varied data sets and uses, educators can piece together a more complete narrative of student success and the impacts of educational interventions.

Master Data Analysis with an M.S. in Learning Sciences From SMU

Whether it is the detailed narratives unearthed through qualitative data or the informative patterns derived from quantitative analysis, both qualitative and quantitative data can provide crucial information for educators and researchers to better understand and improve learning. Dive deeper into the art and science of learning analytics with SMU's online Master of Science in the Learning Sciences program . At SMU, innovation and inquiry converge to empower the next generation of educators and researchers. Choose the Learning Analytics Specialization to learn how to harness the power of data science to illuminate learning trends, devise impactful strategies, and drive educational innovation. You could also find out how advanced technologies like augmented reality (AR), virtual reality (VR), and artificial intelligence (AI) can revolutionize education, and develop the insight to apply embodied cognition principles to enhance learning experiences in the Learning and Technology Design Specialization , or choose your own electives to build a specialization unique to your interests and career goals.

For more information on our curriculum and to become part of a community where data drives discovery, visit SMU's MSLS program website or schedule a call with our admissions outreach advisors for any queries or further discussion. Take the first step towards transforming education with data today.

• Retrieved on August 8, 2024, from nnlm.gov/guides/data-glossary/qualitative-data
• Retrieved on August 8, 2024, from nnlm.gov/guides/data-glossary/quantitative-data
• Retrieved on August 8, 2024, from cdc.gov/healthyyouth/evaluation/pdf/brief19.pdf
• Retrieved on August 8, 2024, from cdc.gov/healthyyouth/evaluation/pdf/brief20.pdf
• Retrieved on August 8, 2024, from lumivero.com/solutions/
• Retrieved on August 8, 2024, from atlasti.com/
• Retrieved on August 8, 2024, from ibm.com/products/spss-statistics
• Retrieved on August 8, 2024, from cran.r-project.org/doc/manuals/r-release/R-intro.html#Introduction-and-preliminaries

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