How to Run Linear Mixed Effects Analysis for Pairwise Comparisons? A Tutorial and a Proposal for the Calculation of Standardized Effect Sizes.

This tutorial provides guidelines for conducting linear mixed effects (LME) analyses for simple designs, aimed at researchers familiar with t-tests, analysis of variance (ANOVA) and linear regression. First, we compare LME analyses with traditional methods when participants are the only source of random variation. We show that LME analysis is more interesting as soon as you have more than one observation per participant per condition. The second section discusses studies where both participants and stimuli are used as sources of random variation, ensuring robust generalization beyond the specific stimuli tested. In our search for standardized effect sizes, we saw that partial eta squared is even less informative for LME than for ANOVA. We present as an alternative, to be used in combination with the traditional measure eta squared (also in ANOVA). To facilitate implementation, we analyze toy datasets with R and jamovi. This tutorial gives researchers a good foundation for LME analyses of simple 2 × 2 designs and paves the way for tackling more complicated designs.