I ran a linear mixed model analysis on my data and specified a rather "simple" LMM. The data come from a within-subject design were participants rated the same stimulus in three different conditions using two questions. The model structure looks like this:
DV ~ Condition * Question + (1 + Condition + Question | Participant)
Condition and question are both dummy coded variables with 3 (Condition) and 2 (Question) levels. I get a significant result for the fixed effect of Condition (but not Question and also no interaction between the two).
I analyze which of my 3 levels in Condition differ from each other and use the emmeans() function to compute contrasts. I see that Condition 1 differs from Condition 2 and from Condition 3.
Now I wanted to calculate an effect size for these differences and I used the eff_size() function to do so. However, the effect sizes I get in the output seem way too big. E.g. for my contrasts comparing Condition 1 and 2 my estimate (which equals the mean difference of both Conditions) has a t-value of 4.795. When calculating the effect size "per hand" I get two values. If I use the formula for drm (Mean2 - Mean1 / SW; where SW = Sdiff / sqrt(2(1-r)) I get a d of d = 0.946. If I use the t-value and calculate d by using d = t/sqrt(N) I get an even smaller value of d = 0.692.
But using eff_size() from emmeans() results in a d = 1.59.
What is the "correct" way for me to get an approximation of d as an effect size in this scenario?