I want to compute an effect size for a fixed factor. In this study, there is one fixed factor with 3 conditions (Consistency). Passage and Subject are random effects. I used a Cohen's d to compute effect sizes comparing two means at a time, but I would like to compute an overall effect size of the fixed factor, Consistency.
What effect size measure is appropriate for a design with one IV and 3 conditions in mixed modeling and how would I write the code to carry out the effect size?
Thank you so much for any help you can provide.
Here is the code I used:
PdatFIN$RT_target <- as.numeric(PdatFIN$RT_target)
PdatFIN$Consistency <- as.factor(PdatFIN$Consistency)
str(PdatFIN)
m <- lmer(RT_target ~ Consistency + (1 | Subject) + (1 | Passage), PdatFIN); summary(m); Anova(m)
lme.dscore(m,data=PdatFIN,type = "lme4")
m.contrasts <- emmeans(m,"Consistency")
pairs(m.contrasts)
And here is my output:
Linear mixed model fit by REML ['lmerMod']
Formula: RT_target ~ Consistency + (1 | Subject) + (1 | Passage)
Data: PdatFIN
REML criterion at convergence: 7314.2
Scaled residuals:
Min 1Q Median 3Q Max
-2.0682 -0.6320 -0.1771 0.5346 4.1376
Random effects:
Groups Name Variance Std.Dev.
Subject (Intercept) 203923 451.6
Passage (Intercept) 23091 152.0
Residual 239054 488.9
Number of obs: 476, groups: Subject, 30; Passage, 18
Fixed effects:
Estimate Std. Error t value
(Intercept) 1711.58 98.75 17.333
Consistency2 427.71 56.19 7.612
Consistency3 173.18 55.99 3.093
Correlation of Fixed Effects:
(Intr) Cnsst2
Consistncy2 -0.301
Consistncy3 -0.303 0.532
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RT_target
Chisq Df Pr(>Chisq)
Consistency 59.216 2 1.385e-13 ***
Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> #Cohens d
> lme.dscore(m,data=PdatFIN,type = "lme4")
t df d
Consistency2 7.612028 432.5373 0.7320127
Consistency3 3.092820 434.6247 0.2967068
> m.contrasts <- emmeans(m,"Consistency")
> pairs(m.contrasts)
contrast estimate SE df t.ratio p.value
Consistency1 - Consistency2 -428 56.2 432 -7.607 <.0001
Consistency1 - Consistency3 -173 56.1 434 -3.090 0.0060
Consistency2 - Consistency3 255 54.3 429 4.688 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
