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Independent Samples t-test



Independent Samples t-test


Researchers use the independent samples t-test to find out if there is a 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).

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

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 in 2025.

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







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The statistical procedure results in a t-value 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).

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


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You can calculate the independent samples t-test by hand. If you are interested, click the download link for a pdf file. [ t-test DOWNLOAD HERE ]
Also, here is an online calculator where you can enter two sets of values and obtain a t-test result.

EasyCalculation.com


Connections and Links to Resources

My Page    www.suttong.com

My Books   AMAZON

FACEBOOK   Geoff W. Sutton

X  @Geoff.W.Sutton

LinkedIN Geoffrey Sutton  PhD

Publications (many free downloads)
     
  Academia   Geoff W Sutton   (PhD)
    
  ResearchGate   Geoffrey W Sutton   (PhD)

_________________________________


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 revised 23 August 2025

































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