Skip to main content

Dependent Samples Matched Pairs t test

 The Dependent Samples t test is used to test for significant differences between two sets of numerical data produced by the same organisms or organisms that are matched on all relevant variables.

Dependent Samples t test Infographic
Geoffrey W. Sutton & AI

What you will find in this article.

1. Basic examples

2. Requirements to use the Dependent Samples t test

3. Two books professors recommend for students

*4. A step by step procedure for calculation of a Dependent Samples t test

*5. A detailed example of a calculation table with step by step calculations

6. An APA style results text.

*7. An Calculator for you to enter your own data

* AI code can contain errors- leave a message if you notice an error.

Example: Same Group- Pre and Posttest

In one example, a group of people who attend a workshop may complete a pretest and a posttest. A Dependent Samples t test can be used to compare the mean differences between the pretest and the posttest.

Example: Two Groups: Matched Pairs

An example of a Matched Pairs t test can be used to compare two groups of people in a reading method experiment. A relevant variable would be reading ability. A reading test could be used to identify people with similar scores. One member of the pair is then randomly assigned to a new reading method group and the matching person is then assigned to the traditional reading group. At the end of the study, a Matched Pairs t test can be used to compare mean scores for the groups.

When the same person produces two sets of scores, each person is their own control. Because of the level of control, there is less variation than would be the case when using different people in each group.

When the groups contain different unmatched people or subjects, the groups are considered independent samples and an Independent Samples t test is used.

Requirements for the Dependent Samples t test

A categorical variable defines the groups

One continuous dependent measure: interval or ratio scale

Paired observations

Normal distribution of the differences in the paired measurements

No extreme outliers

___________

Notes on requirements

A categorical variable has two or more categories like Group 1 and Group 2

Paired observations are those by the same person such as scores on a pre and posttest or two different people who are alike in characteristics relevant to the study.

The data should be close to a normal distribution for example not extremely skewed.

___________

Reference for using scales in research:

Buy Creating Surveys on

GOOGLE BOOKS

 AMAZON 


 

 

 




As an Amazon associate, I earn from qualifying purchases.

Reference for clinicians and students on understanding assessment

Buy Applied Statistics for Counselors

GOOGLE BOOKS

 AMAZON

 


 

 





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  

 __________

Step by Step Calculation of the Dependent t test

Here is the step-by-step procedure revised with text-friendly, easy-to-read formulas that you can easily copy and paste.

1. Find the Difference (D) for Each Pair

For each pair of observations, subtract the second score from the first score. Keep the direction of subtraction consistent.

    Formula: D = Score_1 - Score_2

2. Square Each Difference (D^2)

Multiply each individual difference score by itself.

  Formula: D^2 = D * D

3. Find the Sums

Add up all the difference scores, and add up all the squared difference scores to get your totals.

  Sum of differences: Sum(D)

  Sum of squared differences: Sum(D^2)

4. Calculate the Mean Difference (Mean_D)

Divide the sum of the differences by the total number of pairs (n).

   Formula: Mean_D = Sum(D) / n

5. Calculate the Standard Deviation of the Differences (SD)

Use the totals from Step 3 and the number of pairs to find the variance, then take the square root.

   Formula: SD = square_root( [Sum(D^2) - ((Sum(D) * Sum(D)) / n)] / (n - 1) )

6. Calculate the Standard Error (SE)

Divide the Standard Deviation by the square root of the number of pairs.

   Formula: SE = SD / square_root(n)

7. Compute the t-Statistic

Divide the mean difference by the standard error.

   Formula: t = Mean_D / SE

8. Find Degrees of Freedom (df)

Calculate your degrees of freedom to look up your critical value in a standard t-table.

   Formula: df = n - 1

EXAMPLE

Scenario: Statistics Anxiety Scores

A researcher wants to know if a 1-hour mindfulness seminar reduces statistics anxiety in college students. Anxiety is measured on a scale from 10 to 40 before and after the seminar. A higher score means more anxiety.

1. The Data & Preliminary Calculation Table

Student (n) Pre-Seminar (Score 1) Post-Seminar (Score 2) Difference (D) Squared Diff (D^2)
12418636
22822636
3201911
43225749
52520525
63024636
7222111
82723416
92922749
10211839
Totals (n = 10) Mean = 25.8 Mean = 21.2 Sum(D) = 46 Sum(D^2) = 258

2. Step-by-Step Statistical Calculations

  • Mean Difference (Mean_D):
    Mean_D = Sum(D) / n = 46 / 10 = 4.60
  • Standard Deviation of Differences (SD):
    SD = square_root( [Sum(D^2) - ((Sum(D) * Sum(D)) / n)] / (n - 1) )
    SD = square_root( [258 - ((46 * 46) / 10)] / 9 )
    SD = square_root( [258 - 211.6] / 9 ) = square_root(46.4 / 9) = 2.27
  • Standard Error (SE):
    SE = SD / square_root(n) = 2.27 / square_root(10) = 2.27 / 3.162 = 0.72
  • t-Statistic:
    t = Mean_D / SE = 4.60 / 0.72 = 6.41
  • Degrees of Freedom (df):
    df = n - 1 = 10 - 1 = 9

3. Final Metrics Summary Table

MetricValue
t-Statistic (t)6.41
Degrees of Freedom (df)9
p-value (two-tailed)< .001 (Exact: 0.00012)
Cohen's d (Effect Size)2.03 (Large Effect)

4. Formal APA Manuscript Style Result

"A dependent samples t-test was conducted to evaluate the impact of a mindfulness seminar on students' statistics anxiety scores. There was a statistically significant decrease in anxiety scores from before the seminar (M = 25.80, SD = 4.13) to after the seminar (M = 21.20, SD = 2.70), t(9) = 6.41, p < .001, two-tailed, Cohen’s d = 2.03. These results indicate that the mindfulness seminar successfully reduced short-term statistics anxiety levels among the students."

Dependent Samples t-Test Calculator

Pair # Group 1 ($X_1$) Group 2 ($X_2$)
1
2
3
4
5

Calculation Results

Sample Size ($N$)-
Degrees of Freedom ($df$)-
Mean Difference ($\bar{D}$)-
Std. Deviation ($s_d$)-
Std. Error ($SE$)-
t-Statistic ($t$)-
p-Value (2-Tailed)-
p-Value (1-Tailed)-
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