sphericitásteszt

The sphericity test, often referred to by its German name "Spherizitätstest" or simply sphericity test, is a statistical method used to assess whether a set of paired observations exhibits sphericity. Sphericity is an assumption in certain statistical analyses, most notably in repeated-measures analysis of variance (ANOVA). It assumes that the variances of the differences between all possible pairs of within-subject conditions are equal. In simpler terms, it checks if the variability in the data is consistent across all the different conditions or time points being measured for the same subjects.

Violations of sphericity can lead to an inflated Type I error rate in repeated-measures ANOVA, meaning the test might incorrectly conclude that there is a significant effect when, in reality, there isn't. The sphericity test helps researchers determine if this assumption is met. If sphericity is violated, corrections such as Greenhouse-Geisser or Huynh-Feldt are typically applied to the degrees of freedom to adjust the F-statistic and obtain a more accurate p-value.

Mauchly's test of sphericity is the most common statistical test employed to evaluate this assumption. It produces a p-value, and a statistically significant p-value (typically less than 0.05) indicates that the sphericity assumption has been violated. If the p-value is not significant, the assumption of sphericity is considered to be met. Therefore, the sphericity test plays a crucial role in ensuring the validity of conclusions drawn from repeated-measures statistical designs.