What is mauchly test of sphericity

Show page numbers Download PDF. Search form icon-arrow-top icon-arrow-top. Page Site Advanced 7 of Edited by: Neil J. Buy in print. The Sphericity Assumption. In the situation where epsilon is greater than 0. It returns ANOVA table that has been automatically corrected for eventual deviation from the sphericity assumption in a design containing repeated measures factors.

This article describes the basics of sphericity assumption. Prerequisites Make sure that you have installed the following R packages: tidyverse for data manipulation and visualization ggpubr for creating easily publication ready plots rstatix provides pipe-friendly R functions for easy statistical analyses datarium : contains required data sets for this chapter Start by loading the following required R packages: library tidyverse library ggpubr library rstatix.

Measuring sphericity The procedure is as follow: Calculate the differences between each combination of related groups Compute the variance of each group difference R codes: 1. Compute group differences grp. Compute the variances grp. Key arguments : data : data frame dv : numeric the dependent or outcome variable name. The null hypothesis is that the variances of the group differences are equal.

Sphericity corrections results to be considered in case we could not maintain the sphericity assumption. Two common corrections used in the literature are provided: Greenhouse-Geisser epsilon GGe , and Huynh-Feldt epsilon HFe and their corresponding p-values. Sphericity refers to the condition where the variances of the differences between all combinations of related groups are equal.

If this assumption is violated, then the F-ratio becomes inflated and the results of the repeated measures ANOVA become unreliable. If the p-value of the test is less than some significance level e. Otherwise, if the p-value is not less than some significance level e. For example, suppose a doctor measures the resting heart rate of subjects during three different time points:.

He wants to perform a repeated measures ANOVA to see if there is a significant difference in mean resting heart rate across these three time points. The following table shows the results of his data collection:.