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

Area of Science:

• Statistics
• Psychology
• Behavioral Science

Background:

• Traditional statistical methods like t-tests, ANOVA, and linear regression have limitations with complex data structures.
• Linear mixed effects (LME) models offer a flexible framework for analyzing data with non-independent observations, such as repeated measures.
• Researchers often need guidance on implementing LME for simple designs and interpreting effect sizes.

Purpose of the Study:

• To provide a practical tutorial on conducting linear mixed effects (LME) analyses for simple experimental designs.
• To compare LME with traditional statistical methods (t-tests, ANOVA, linear regression) in scenarios with varying sources of random variation.
• To introduce and evaluate standardized effect size measures suitable for LME, addressing limitations of traditional measures like partial eta squared.

Main Methods:

• Comparison of LME analyses with traditional methods for designs with participants as the sole source of random variation.
• Extension of LME analysis to designs incorporating both participants and stimuli as sources of random variation for enhanced generalizability.
• Demonstration of LME implementation using toy datasets in R and jamovi, including calculation of novel effect size metrics like eta squared within.

Main Results:

• LME analyses are shown to be more informative than traditional methods when multiple observations per participant exist.
• Partial eta squared is found to be less informative in LME than in ANOVA.
• Eta squared within is proposed as a valuable alternative effect size measure for LME, complementing traditional eta squared.

Conclusions:

• This tutorial equips researchers with the foundational knowledge for applying LME to simple 2x2 designs.
• The presented methods and effect size measures facilitate robust statistical analysis and interpretation in LME.
• The tutorial serves as a stepping stone for researchers to confidently tackle more complex LME designs in future studies.