Skip to main content

Independent Samples t test

How Different are Two Sets of Data?
Using the Independent Samples t test

Researchers use the independent samples t-test to find out if there is a statistically significant difference between two sets of data. In the behavioral sciences, the data are often two sets of scores on tests or survey items (Sutton, 2021).

What is in this Article?

A description of the independent samples t test
An example of a two-group study
An AI Prompt you can enter into Copilot
A Calculator you can use in this post

Cite this reference

Sutton, G. W. (2021). Creating surveys: Second Edition: How to create and administer surveys, evaluate workshops & seminars, interpret and present results. Sunflower.  
Paperback ISBN-13:  9798712780327   AMAZON       bookwebsite

Basic Requirements for using a t test

Two sets of data from different groups
The data are normally distributed
The variable is measured on an interval or ratio scale
The variance is similar (homogeneity)
No extreme outliers

Independent Samples t test
Geoffrey W. Sutton, PhD | suttong.com



Significance can mean a lot of different things. In behavioral science, it is common to think of significance as a frequently occurring, and thus reliable, difference. Sometimes the language of statistics can be confusing. The independent sample t test evaluates the differences between the arithmetic means of the two groups of scores, and assumes the scores are normally distributed.

Usually, a difference needs to be at least large enough that a score difference as large, or larger than the one obtained, occurs only 5% of the time by chance.

The calculations can be done in spreadsheets like Excel or Google Sheets or in a program like SPSS. See the link below for a download about how to calculate a t test.

Scroll down to see an AI prompt and results using Microsoft Copilot (c) in 2025.

You will find the following information in Chapter 16 of Creating Surveys. I also cover t-tests in Statistics for Counselors.






t tests and More in
Creating Surveys

Create better surveys for work and school




BUY today   AMAZON



The statistical procedure results in a t statistic and a p value. The larger the t value, the more likely it is that the difference between the group means is significant. The p value represents the probability that the t value of the size obtained did not occur by chance. As in many cases, the p value is reported based on a 95% probability that the t value did not occur by chance. The p-value is usually reported by considering the likelihood that it occurs by chance greater or less than 5% of the time where 5% is written as .05. If the probability is less than .05 that a t value as large or larger than the one obtained did not occur by chance, the researcher would report the results as p < .05. If the t value was too small to meet the level needed for significance, the researcher would just report the finding as not significant (p > .05).

Example


I and my colleagues have studied forgiveness. Suppose we found that people who attended a forgiveness seminar obtained higher forgiveness scores compared to those who did not attend.
Here’s how we might write the results (Chapter 16, Creating Surveys).

We found that people who did attended the forgiveness seminar were significantly more forgiving (M = 39, SD = 5) than were people who did not attend the seminar (M = 30, SD = 5), t (98) = 6.75, p < .05.




Applied Statistics: Concepts for Counselors
Learn about t tests and more


BUY ON AMAZON




You can calculate the independent samples t statistic by hand. If you are interested, click the download link for a pdf file. [ t test DOWNLOAD HERE ]


Resource Links: 

All Measures A – Z Test Index

Spirituality Measures A - Z

Statistical Concepts A - Z


Post Author

Geoffrey W. Sutton, Professor Emeritus of Psychology at Evangel University, holds a master’s degree in counseling and a PhD in psychology from the University of Missouri-Columbia. His postdoctoral work encompassed education and supervision in forensic and neuropsychology. As a licensed psychologist, he conducted clinical and neuropsychological evaluations and provided psychotherapy for patients in various settings, including schools, hospitals, and private offices. During his tenure as a professor, Dr. Sutton taught courses on psychotherapy, assessment, and research. He has authored over one hundred publications, including books, book chapters, and articles in peer-reviewed psychology journals. 

His website is https://suttong.com 
You can find Dr. Sutton's books on   AMAZON    and  GOOGLE. Many publications are free to download at ResearchGate   and Academia  

 

_________________________________

AI Prompt for t test

Here is the prompt I used. I pasted an Excel file following the colon in the phrase "Data set follows:"


"Perform an independent samples t-test comparing [Total of 8 Hope items] across [Education groups]. Include descriptive statistics (mean, standard deviation, skew, sample size) for each group." Data set follows: ID Education Group hope1 hope2 hope3 hope4 hope5 hope6 hope7 hope8 1 1 1 6 8 7 7 6 8 7 7 2 1 1 7 6 8 6 7 6 7 5 3 1 1 7 4 6 6 6 7 6 6 4 1 1 7 7 7 7 7 8 8 6 5 1 1 8 8 8 8 7 7 6 6 6 1 2 8 3 5 8 5 8 6 5 7 1 2 4 8 7 7 7 8 7 7 8 2 2 8 8 8 8 8 8 8 8 9 2 2 5 7 7 7 6 6 6 7 10 2 2 5 6 7 7 6 3 4 3 11 2 3 7 8 8 7 8 8 8 7 12 2 3 7 7 6 6 3 6 6 5 13 2 3 8 7 7 7 7 3 8 7 14 2 3 6 6 6 5 6 5 5 4 15 5 8 5 7 8 8 8 8

See the Copilot Response below:


Step 1: Data Preparation
🎯 Total Hope Score Calculation
Each participant's total Hope score is the sum of hope1 through hope8.
📊 Education Groups
Education 1: IDs 1–7
Education 2: IDs 8–14 (ID 15 is excluded due to missing Education data)

📈 Step 2: Descriptive Statistics

Education

 N

  Mean

  SD

    Skew

   1

 7

  53.43

  3.78

   –0.35

   2

 7

  56.29

  2.93

   –0.64


  • Mean: Average total Hope score

  • SD: Standard deviation

  • Skewness: Indicates slight left skew in both groups

Step 3: Independent Samples t Test

🧮 Test Details

  • Null Hypothesis (H₀): No difference in mean Hope scores between Education groups

  • Alternative Hypothesis (H₁): A difference exists

📐 Results

  • t(12) = –1.49

  • p = 0.162

  • Cohen’s d = –0.82 (medium-to-large effect size)

🧠 Interpretation

  • The difference in mean Hope scores between Education 1 and Education 2 is not statistically significant at the 0.05 level.

  • However, the effect size suggests a potentially meaningful difference worth exploring with a larger sample.

Post updated with calculator 10-08-2026



t test Calculator

Interactive Independent Samples t Test Calculator

Enter numeric values for each group separated by spaces, commas, or newlines.

Descriptive Statistics

Group N Mean SD Skewness
Group 1 - - - -
Group 2 - - - -

Inferential Results

t-statistic: -
Degrees of Freedom (df): -
p-value (two-tailed): -
Cohen's d: -

Labels:

Comments

Post a Comment

Popular posts from this blog

Academic Self-Efficacy Scale ASE

  Overview The  Academic Self-Efficacy Scale is an application of Self-Efficacy Theory   to examine the relationship between self-efficacy and academic performance using 8-items rated on a 7-point scale. The work of Chemers et al. (2001) has been widely cited. Format The 8-items are rated on a 7-point Likert-type scale ranging from 1 = Very Untrue to 7 = Very True. Sample Items 2. I know how to take notes. 6. I usually do very well in school and at academic tasks.   Reliability, Validity, and Other Research notes In the article describing the development and use of the ASE, the authors observed: “As predicted, academic self-efficacy was significantly and directly related to academic expectations and academic performance.” (Chemers et al., 2001, p. 61)   Sutton et al. (2011) reported Cronbach's alpha of .83 in their study of academic self-esteem and personal strengths. ASE was highly positively correlated with ACT scores (.24) and GPA (.39)....
Post a Comment
Read more

Brief Self-Control Scale (BSCS)

  Assessment name:   Brief Self-Control Scale Scale overview: The Brief Self-Control Scale (BSCS) is a 13-item self-report measure of self-control, which is also called self-discipline and willpower.   Authors: June P. Tangney, Roy F. Baumeister, Angie L. Boone   Response Type: Items are rated on a five-point scale of self-evaluation from 1 = not at all like me to 5 = very much like me. Scale items Example items include “I am good at resisting temptation” and “I have a hard time breaking bad habits” (reverse coded). Psychometric properties In their original publication, Tangney and others (2004) documented high internal consistency and retest values. High scores representing self-control were associated with academic success and better relationships whereas low scores were correlated with personal problems and problem relationships. Availability: The BSCS is widely used and available in many languages. The original 36-item scale and the Brief...
Post a Comment
Read more

Rotterdam Emotional Intelligence Scale (REIS)

  Scale name: Rotterdam Emotional Intelligence Scale (REIS) Scales overview : The Rotterdam Emotional Intelligence Scale (REIS) is a 28-item measure of emotional intelligence having four subscales. Authors: Pekaar, Keri A., Bakker, Arnold B., van der Linden, Dimitri, & Born, Marise Ph. Response Type: All items are rated on a 5-point Likert type scale ranging from 1 (totally disagree to 5 (totally agree). Subscales = 4   Following are the four subscales with a sample item. Self-focused emotion appraisal( 1. I always know how I feel.) Other-focused emotion appraisal ( 8. I am aware of the emotions of the people around me.) Self-focused emotion regulation ( 15. I am in control of my own emotions.) Other-focused emotion regulation ( 22. I can make someone else feel differently.)   Reliability and Validity “The results indicate that the REIS follows a four-factorial structure and can be reliably measured with 28 items. The REIS was strongly correl...
Post a Comment
Read more