Table 1

Statistical tests used to analyze data

	Data structure	Type of test	Post-hoc power
a	Normal	2 × 2 ANOVA	0.06
b	Negative binomial (overdispersed count)	GLMM, RI, and S	^a
c	Normal	2 × 2 × 6 repeated-measures ANOVA	0.27
d	Negative binomial	GLMM, RI, and S with UCS matrix	^a
e	Negative binomial	GLMM, RI, and S with UCS matrix (test of simple effects)	^a
f	Negative binomial	GLMM, RI, and S with UCS matrix (Bonferroni-corrected post-hoc comparisons)	^a
g	Negative binomial	GLMM, RI, and S with UCS matrix (test of simple effects)	^a
h	Negative binomial	GLMM, RI, and S with UCS matrix (Bonferroni-corrected post-hoc comparisons)	^a
i	Negative binomial	GLMM, RI, and S with UCS matrix (test of simple effects)	^a
j	Negative binomial	GLMM, RI, and S with UCS matrix	^a
k	Negative binomial	GLMM, RI, and S with UCS matrix (test of simple effects)	^a
l	Negative binomial	GLMM, RI, and S with UCS matrix (Bonferroni-corrected post-hoc comparisons)	^a
m	Negative binomial	GLMM, RI, and S with UCS matrix (Bonferroni-corrected post-hoc comparisons)	^a
n	Negative binomial	GLMM, RI	^a
o	Binomial	GLMM, RI, and S with UCS matrix	^a
p	Negative binomial	GLMM, RI, and S with UCS matrix	^a
q	Normal	GLMM, RI, and S	^a
r	Normal	GLMM, RI, and S with UCS matrix	^a
s	Normal	GLMM, RI, and S with UCS matrix (Bonferroni-corrected post-hoc comparisons)	^a
t	Binomial	GLMM, RI	^a
u	Negative binomial	GLMM, RI, and S	^a
v	Log-transformed normal	GLMM, RI, and S	^a
w	Binomial	GLMM, RI, and S with UCS matrix	^a
x	Negative binomial	GLMM, RI, and S with UCS matrix	^a
y	Normal	GLMM, RI, and S	^a
z	Normal	GLMM, RI, and S with UCS matrix	^a
aa	Binomial	GLMM, RI	^a
bb	Binomial	GLMM, RI	^a
cc	Negative binomial	GLMM, RI, and S	^a
dd	Log-transformed normal	GLMM, RI, and S	^a
ee	No assumptions made	Spearman’s ρ nonparametric correlation	>0.96^b
ff	No assumptions made (underlying distributions unknown; high kurtosis and skew)	Wilcoxon rank sum nonparametric test (two-sample Mann–Whitney)	0.05, 0.07^c
gg	Proportions	Fisher's exact test for cross-tabs	0.12
hh	Normal	Independent samples t tests, equal variances (tested by Levene’s test)	0.08, 0.08, and 0.09
ii	No assumptions made (goal-tracker distribution non-normal)	Wilcoxon rank sum nonparametric test (two-sample Mann–Whitney)	1.00^c

GLMM, generalized linear mixed model; RI, random intercept; S, random slope (of repeated measure; UCS, unstructured covariance matrix between random effects (UCS matrix; covariance was fixed to zero in other GLMM models). Estimates of observed (post hoc) power are for experimentally relevant interaction effects.
↵a Estimates for main effects and interactions in GLMMS with RI and/or S, and for normally distributed data with RI and S are not readily calculable. This is the result of the complex, nonclosed form nature of optimizations of GLMMs with multiple random effects, which renders estimation of power not directly derivable, nor estimation via brute force, highly repeated simulation readily feasible.
↵b Simulation assumes normal distributions.
↵c Simulations assume (fitted) Weibull distributions.