Spherizitätstest

The Spherizitätstest, also known as the sphericity test, is a statistical procedure used primarily in the context of repeated measures analysis of variance (ANOVA) to assess whether the variances of the differences between groups are equal. This test is particularly relevant when analyzing data from within-subjects or mixed-design experiments, where multiple measurements are taken from the same subjects under different conditions.

The term "sphericity" refers to the assumption that the variances of the differences between all possible pairs of within-subject factors are equal. When this assumption holds, the degrees of freedom for the F-tests in repeated measures ANOVA can be calculated using simple formulas, leading to more accurate and reliable results. If sphericity is violated, the Type I error rate may be inflated, meaning the likelihood of falsely rejecting the null hypothesis increases.

The Spheritzitätstest is often conducted using Mauchly’s test of sphericity, which is based on the multivariate normality of the data and is sensitive to sample size. If Mauchly’s test indicates a violation of sphericity, adjustments such as Greenhouse-Geisser, Huynh-Feldt, or lower-bound corrections are commonly applied to the degrees of freedom to control for inflated Type I error rates. These corrections reduce the degrees of freedom, making the test more conservative.

While Mauchly’s test is widely used, its reliance on normality and sensitivity to sample size has led researchers to explore alternative approaches, such as visual inspection of plots or non-parametric alternatives. Despite its limitations, the Spherizitätstest remains a fundamental step in ensuring the validity of repeated measures ANOVA results. Proper interpretation and adjustment of sphericity violations are essential for maintaining the integrity of statistical conclusions in experimental research.