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 Transform.
3. Click Compute Variable.
4. In the Target Variable: box, give the outcome variable a name with a "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 Numeric Expression: box.
7. Click on the "-" button or simply type "-" in the Numeric Expression: box.
8. Click on the second observation of the continuous outcome to highlight it.
9. Click on the arrow to bring it into the Numeric Expression: box.
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 Analyze.
13. Drag the cursor over the Descriptive Statistics drop-down menu.
14. Select Descriptives.
15. Click on the difference scores variable to highlight it.
16. Click on the arrow to move the variable into the Variable(s): box.
17. Click the Options tab.
18. Deselect Minimum and Maximum boxes under the Dispersion section.
19. Select the Kurtosis and Skewness boxes under the Distribution section.
20. Click Continue.
21. Select the Save standardized values as variables box.
22. Click OK.
2. Click Transform.
3. Click Compute Variable.
4. In the Target Variable: box, give the outcome variable a name with a "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 Numeric Expression: box.
7. Click on the "-" button or simply type "-" in the Numeric Expression: box.
8. Click on the second observation of the continuous outcome to highlight it.
9. Click on the arrow to bring it into the Numeric Expression: box.
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 Analyze.
13. Drag the cursor over the Descriptive Statistics drop-down menu.
14. Select Descriptives.
15. Click on the difference scores variable to highlight it.
16. Click on the arrow to move the variable into the Variable(s): box.
17. Click the Options tab.
18. Deselect Minimum and Maximum boxes under the Dispersion section.
19. Select the Kurtosis and Skewness boxes under the Distribution section.
20. Click Continue.
21. Select the Save standardized values as variables box.
22. 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?
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