# Normality and repeated-measures t-test

## Assess normality of difference scores when comparing two observations of a continuous outcome

The assumption of normality of difference scores is the first statistical assumption that needs to be tested when comparing two observations of a continuous outcome with a repeated-measures t-test. Normality of difference scores is assessed using skewness and kurtosis statistics. In order to meet the statistical assumption of normality, skewness and kurtosis statistics should be below an absolute value of 2.0. If either skewness or a kurtosis statistic is above an absolute value of 2.0, then the continuous distribution is assumed to not be normal. Oftentimes, if the distributions for the "pre" observation and the "post" observation are normally distributed, the difference scores will be normally distributed. Repeated-measures t-tests should not be conducted on continuous observations that violate the assumption of normality of difference scores. Repeated-measures t-tests should only be conducted on continuous observations of an outcome that are normally distributed.

### The steps for conducting skewness and kurtosis statistics on difference scores in SPSS

1. The data is entered in a within-subjects fashion.

2. Click

3. Click

4. In the

5. Click on the first observation of the continuous outcome to highlight it.

6. Click on the

7. Click on the "

8. Click on the second observation of the continuous outcome to highlight it.

9. Click on the

10. Click

11. Go to

12. Click

13. Drag the cursor over the

14. Select

15. Click on the difference scores variable to highlight it.

16. Click on the

17. Click the

18. Deselect

19. Select the

20. Click

21. Select the

22. Click

2. Click

**.**__T__ransform3. Click

**.**__C__ompute Variable4. In the

**box, give the outcome variable a name with a "**__T__arget Variable:**D**" in front of it. Example: "**DOutcome**"5. Click on the first observation of the continuous outcome to highlight it.

6. Click on the

**arrow**to bring it into the**Num**box.__e__ric Expression:7. Click on the "

**-**" button or simply type "-" in the**Num**box.__e__ric Expression:8. Click on the second observation of the continuous outcome to highlight it.

9. Click on the

**arrow**to bring it into the**Num**box.__e__ric Expression:10. Click

**OK**.11. Go to

**Data View**and there is a new variable that contains the difference scores between the two observations of the continuous outcome.12. Click

**.**__A__nalyze13. Drag the cursor over the

**D**drop-down menu.__e__scriptive Statistics14. Select

**.**__D__escriptives15. Click on the difference scores variable to highlight it.

16. Click on the

**arrow**to move the variable into the**box.**__V__ariable(s):17. Click the

**tab.**__O__ptions18. Deselect

**Mi**and__n__imum**Ma**boxes under the__x__imum**Dispersion**section.19. Select the

**and**__K__urtosis**Ske**boxes under the__w__ness**Distribution**section.20. Click

**Continue**.21. Select the

**Save standardi**box.__z__ed values as variables22. Click

**OK**.### The steps for interpreting the SPSS output for skewness and kurtosis statistics

1. Under the

**skewness**and**kurtosis**columns of the**Descriptive Statistics**table, if the**Statistic is less than an absolute value of 2.0**, then researchers can assume**normality**of the difference scores.### Was the assumption of normality of difference scores met for repeated-measures t-test?

## Hire A Statistician - Statistical Consulting for Students

**DO YOU NEED TO HIRE A STATISTICIAN?**

Eric Heidel, Ph.D.

**will provide the following statistical consultingservices for undergraduate and graduate students at $50/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.**

- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics