Sphericity and repeated-measures ANOVA
Greenhouse-Geisser correction is used when sphericity is violated
The assumption of sphericity is often not met when conducting repeated-measures ANOVA analyses. For practical purposes, the Greenhouse-Geisser correction is often used to correct for the violation of the assumption of sphericity. Sphericity relates to the artificial inflation or deflation of covariance matrices associated with correlated measurements of an outcome.
The steps for checking the assumption of sphericity in SPSS
1. Click Analyze.
2. Drag the cursor over the General Linear Model drop-down menu.
3. Click on Repeated Measures.
4. Type the number of observations of the continuous outcome being collected.
5. Click the Add button.
6. Click the Define button.
7. Click on the first observation of the continuous outcome.
8. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
9. Click on the second observation of the continuous outcome.
10. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
11. Click on the third observation of the continuous outcome.
12. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
13. Click OK.
2. Drag the cursor over the General Linear Model drop-down menu.
3. Click on Repeated Measures.
4. Type the number of observations of the continuous outcome being collected.
5. Click the Add button.
6. Click the Define button.
7. Click on the first observation of the continuous outcome.
8. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
9. Click on the second observation of the continuous outcome.
10. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
11. Click on the third observation of the continuous outcome.
12. Click on the arrow to move the outcome variable into the Within-Subjects Variables: box.
13. Click OK.
The steps for interpreting the SPSS output for the assumption of sphericity
1. In the Mauchly's Test of Sphericity table, look at the value under the Sig. column. This is the p-value that is interpreted.
If the p-value is LESS THAN .05, then researchers have violated the assumption of sphericity.
If the p-value is MORE THAN .05, then researchers have not violated the assumption of sphericity.
If the p-value is LESS THAN .05, then researchers have violated the assumption of sphericity.
If the p-value is MORE THAN .05, then researchers have not violated the assumption of sphericity.
Was the assumption of sphericity met for repeated-measures ANOVA?
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