Transformations for repeated-measures ANOVA
Account for non-normal distributions when comparing three observations
The assumption of normality of differences scores needs to be met when conducting repeated-measures ANOVA. If the difference scores are non-normal, there are really two viable options.
1. Identify any outliers (values that are more than 3.29 standard deviations away from the mean) for each observation of the outcome. If the amount of outliers does not make up more than 10% of all observations, then researchers can delete the outliers in a "listwise" fashion. This means that they delete the observation outright. This is the much less preferable to option two below.
2. Researchers can run a non-parametric Friedman's ANOVA test. Non-parametric tests are robust enough to handle violations of normality and still yield an interpretable p-value and effect. Wilcoxon tests will need to be used in the instance that a significant main effect is found for post hoc comparisons.
1. Identify any outliers (values that are more than 3.29 standard deviations away from the mean) for each observation of the outcome. If the amount of outliers does not make up more than 10% of all observations, then researchers can delete the outliers in a "listwise" fashion. This means that they delete the observation outright. This is the much less preferable to option two below.
2. Researchers can run a non-parametric Friedman's ANOVA test. Non-parametric tests are robust enough to handle violations of normality and still yield an interpretable p-value and effect. Wilcoxon tests will need to be used in the instance that a significant main effect is found for post hoc comparisons.
The steps for conducting Friedman's ANOVA in SPSS
1. The data is entered in a within-subjects fashion.
2. Click Analyze.
3. Drag the cursor over the Nonparametric Tests drop-down menu.
4. Drag the cursor over the Legacy Dialogs drop-down menu.
5. Click K Related Samples.
6. Click on the first observation of the dichotomous categorical outcome.
7. Click on the arrow button to move the first observation of the dichotomous categorical outcome variable into the Test Variables: box.
8. Click on the second observation of the dichotomous categorical outcome.
9. Click on the arrow button to move the second observation of the dichotomous categorical outcome variable into the Test Variables: box.
10. Click on the third observation of the dichotomous categorical outcome.
11. Click on the arrow button to move the third observation of the dichotomous categorical outcome variable into the Test Variables: box..
12. Click OK.
2. Click Analyze.
3. Drag the cursor over the Nonparametric Tests drop-down menu.
4. Drag the cursor over the Legacy Dialogs drop-down menu.
5. Click K Related Samples.
6. Click on the first observation of the dichotomous categorical outcome.
7. Click on the arrow button to move the first observation of the dichotomous categorical outcome variable into the Test Variables: box.
8. Click on the second observation of the dichotomous categorical outcome.
9. Click on the arrow button to move the second observation of the dichotomous categorical outcome variable into the Test Variables: box.
10. Click on the third observation of the dichotomous categorical outcome.
11. Click on the arrow button to move the third observation of the dichotomous categorical outcome variable into the Test Variables: box..
12. Click OK.
The steps for interpreting the SPSS output for Friedman's ANOVA
1. In the Test Statistics table, look at the p-value associated with Asymp. Sig. row. This is the p-value that is interpreted.
If it is LESS THAN .05, then researchers have evidence of a statistically significant effect in the dichotomous categorical outcome across time or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence that there is NOT a statistically significant effect in the dichotomous categorical outcome across time or within-subjects.
If it is LESS THAN .05, then researchers have evidence of a statistically significant effect in the dichotomous categorical outcome across time or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence that there is NOT a statistically significant effect in the dichotomous categorical outcome across time or within-subjects.
If a significant main effect is found, then subsequent Wilcoxon tests should be employed in a post hoc to establish within-subjects differences.
The steps for conducting post hoc Wilcoxon tests in SPSS
1. The data is entered in a within-subjects fashion.
2. Click Analyze.
3. Drag the cursor over the Nonparametric Tests drop-down menu.
4. Drag the cursor over the Legacy Dialogs drop-down menu.
5. Click 2 Related Samples.
6. Click on the first observation of the ordinal outcome to highlight it.
7. Click on the arrow button to move the first observation of the outcome variable into the Test Pairs box under the Variable1 column, Pair 1.
8. Click on the second observation of the ordinal outcome to highlight it.
9. Click on the arrow button to move the second observation of the outcome variable into the Test Pairs box under the Variable2 column, Pair 1.
10. Click on the second observation of the ordinal outcome to highlight it.
11. Click on the arrow button to move the second observation of the outcome variable into the Test Pairs box under the Variable1 column, Pair 2.
12. Click on the third observation of the ordinal outcome to highlight it.
13. Click on the arrow button to move the third observation of the outcome variable into the Test Pairs box under the Variable2 column, Pair 2.
14. Click on the first observation of the ordinal outcome to highlight it.
15. Click on the arrow button to move the first observation of the outcome variable into the Test Pairs box under the Variable1 column, Pair 3.
16. Click on the third observation of the ordinal outcome to highlight it.
17. Click on the arrow button to move the third observation of the outcome variable into the Test Pairs box under the Variable2 column, Pair 3.
18. Click OK.
2. Click Analyze.
3. Drag the cursor over the Nonparametric Tests drop-down menu.
4. Drag the cursor over the Legacy Dialogs drop-down menu.
5. Click 2 Related Samples.
6. Click on the first observation of the ordinal outcome to highlight it.
7. Click on the arrow button to move the first observation of the outcome variable into the Test Pairs box under the Variable1 column, Pair 1.
8. Click on the second observation of the ordinal outcome to highlight it.
9. Click on the arrow button to move the second observation of the outcome variable into the Test Pairs box under the Variable2 column, Pair 1.
10. Click on the second observation of the ordinal outcome to highlight it.
11. Click on the arrow button to move the second observation of the outcome variable into the Test Pairs box under the Variable1 column, Pair 2.
12. Click on the third observation of the ordinal outcome to highlight it.
13. Click on the arrow button to move the third observation of the outcome variable into the Test Pairs box under the Variable2 column, Pair 2.
14. Click on the first observation of the ordinal outcome to highlight it.
15. Click on the arrow button to move the first observation of the outcome variable into the Test Pairs box under the Variable1 column, Pair 3.
16. Click on the third observation of the ordinal outcome to highlight it.
17. Click on the arrow button to move the third observation of the outcome variable into the Test Pairs box under the Variable2 column, Pair 3.
18. Click OK.
The steps for interpreting the SPSS output for post hoc Wilcoxon tests
1. In the Test Statistics table, look at the p-value associated with Asymp. Sig. (2-tailed) row. This is the p-value that is interpreted.
If it is LESS THAN .05, then researchers have evidence of a statistically significant effect in the ordinal outcome across time or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence that there is NOT a statistically significant effect in the ordinal outcome across time or within-subjects.
If it is LESS THAN .05, then researchers have evidence of a statistically significant effect in the ordinal outcome across time or within-subjects.
If the p-value is MORE THAN .05, then researchers have evidence that there is NOT a statistically significant effect in the ordinal outcome across time or within-subjects.
Click on the Download Database and Download Data Dictionary buttons for a configured database and data dictionary for transformations for repeated-measures ANOVA.
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