Final answer:
Assuming sphericity in repeated measures ANOVA means assuming equal variances in differences between conditions. Violating sphericity can lead to biased results. Statistical techniques like Greenhouse-Geisser correction can be used to account for sphericity violation.
Step-by-step explanation:
When we assume sphericity in repeated measures (within-group ANOVA), we are assuming that the variances of the differences between all possible pairs of within-group conditions are equal. This means that the differences between the conditions are roughly the same, and there is no significant interaction effect between the conditions.
If we violate sphericity, it means that the assumption of equal variances of the differences between conditions is not met. This can happen when the differences between conditions are not consistent or when there is a significant interaction effect. Violating sphericity can lead to biased results and incorrect conclusions in the analysis.
To account for sphericity violation, researchers can use statistical techniques such as the Greenhouse-Geisser correction or the Huynh-Feldt correction to adjust the degrees of freedom and p-values in the analysis.