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

Abstract

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 eta squared within 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.

Keywords: Face perception; Mathematical modelling; Statistical analysis.

Figure 1

Violin plot of the data listed in Table 2.

Figure 2

jamovi output for the t-test of working memory capacity between two age groups.

Figure 3

Output jamovi ANOVA between-groups analysis working memory capacity.

Figure 4

Output jamovi linear regression analysis of between-groups example working memory.

Figure 5

Output jamovi LME analysis of between-groups example working memory.

Figure 6

Violin plot of the data shown in Table 6. Lines represent related observations.

Figure 7

Output jamovi t-test longitudinal study working memory.

Figure 8

Output jamovi ANOVA longitudinal study working memory.

Figure 9

Output jamovi LME analysis longitudinal study working memory.

Figure 10

Interaction between Day and Stimulus type. The figure includes the standard errors around the means (based on jamovi).

Figure 11

Output jamovi ANOVA 2 × 2 repeated-measures design.

Figure 12

Jamovi output for an ANOVA on the participant centered values from Table 12.

Figure 13

Output jamovi LME analysis 2 × 2 repeated-measures design.

Figure 14

Average ratings of the young and old group per stimulus.

Figure 15

Output jamovi LME analysis face rating study.

Figure 16

Figure of reading times as a function of Language and Background knowledge.