A skeletal response to a twitter question:
“ANOVA (time point x group) or ANCOVA (group with time point as a covariate) for intervention designs? Discuss.”
follow-up “Only 2 time points in this case (pre- and post-intervention), and would wanna basically answer the question of whether out of the 3 intervention groups, some improve on measure X more than others after the intervention”
Here I compare five methods using fake pre-post data, including
Set up Normal distribution Type I error Power Right skewed continuous – lognormal What the parameterizations look like Type I error Power This 1990-wants-you-back doodle explores the effects of a Normality Filter – using a Shapiro-Wilk (SW) test as a decision rule for using either a t-test or some alternative such as a 1) non-parametric Mann-Whitney-Wilcoxon (MWW) test, or 2) a t-test on the log-transformed response.
I was googling around and somehow landed on a page that stated “When effect coding is used, statistical power is the same for all regression coefficients of the same size, whether they correspond to main effects or interactions, and irrespective of the order of the interaction”. Really? How could this be? The p-value for an interaction effect is the same regardless of dummy or effects coding, and, with dummy coding (R’s default), the power of the interaction effect is less than that of the coefficients for the main factors when they have the same magnitude, so my intuition said this statement must be wrong.
Update to the earlier post, which was written in response to my own thinking about how to teach stastics to experimental biologists working in fields that are dominated by hypothesis testing instead of estimation. That is, should these researchers learn GLMs or is a t-test on raw or log-transformed data on something like count data good enough – or even superior? My post was written without the benefit of either [Ives](Ives, Anthony R.
Motivator: A twitter comment “Isn’t the implication that the large effect size is a direct byproduct of the lack of power? i.e. that if the the study had more power, the effect size would have been found to be smaller.”1 2
A thought: our belief in the magnitude of an observed effect should be based on our priors, which, hopefully, are formed from good mechanistic models and not sample size“.3
