What happens if sphericity is violated in ANOVA?

If the sphericity assumption is violated, the P value in a standard ANOVA table will underestimate the true P value and increase the likelihood of a Type I error. To correct for a sphericity violation, it is necessary to compute a new P value that accounts for the departure from sphericity.

What should you do if the assumption of sphericity is violated?

If, however, the assumption of sphericity is violated, the F-statistic is positively biased rendering it invalid and increasing the risk of a Type I error. To overcome this problem, corrections must be applied to the degrees of freedom (df), such that a valid critical F-value can be obtained.

What does it mean if Mauchly’s test of sphericity is violated?

The violation of sphericity occurs when it is not the case that the variances of the differences between all combinations of the conditions are equal. If sphericity is violated, then the variance calculations may be distorted, which would result in an F-ratio that is inflated.

Which test checks whether the sphericity assumption in a repeated measures ANOVA is violated?

ᵃ Mauchly’s test of sphericity indicates that the assumption of sphericity is violated (p < . 05). The actual results of the repeated measures ANOVA are presented in the Tests of Within-Subjects Effects table.

How do I report a violation of sphericity?

Repeated Measures ANOVA – APA Style Reporting of the sphericity assumption, χ2(2) = 7.17, p = 0.028.” If sphericity is violated, report the Greenhouse-Geisser ε and which corrected results you’ll report: “Since sphericity is violated (ε = 0.840), Huyn-Feldt corrected results are reported.”

What does it mean when Mauchly’s test is significant?

→ If Mauchly’s test statistic is significant (i.e. has a probability value less than . 05) we conclude that there are significant differences between the variance of differences: the condition of sphericity has not been met.

What does it mean if sphericity is met?

” sphericity assumption is met (p>0.05) ” It just means that your data is not sufficient to detect a (more or less particular kind of) violation with sufficient confidence.

How do I report assumption of sphericity?