Bradley's liberal criterion

Question

I'm reading an article where the authors utilized Bradley's liberal criterion to estimate the robustness of the F statistic in the context of post hoc tests.

The problem here is that they said the following:
"Estimators’ power to detect statistical differences among groups was better when Type I error was near 5% (see Pedrosa et al., 2015 for a similar approach) based on Bradley’s liberal criterion, according to which Type I error rate higher than 5.25 is considered conservative and lower than 4.75 liberal (Bradley, 1978)."

But when I go to Bradley's paper, the liberal criterion that he proposed states that p is between 0.5 * alpha and 1.5 * alpha (0.025 and 0.075 when alpha is 0.05), which is a much wider range. Also, the authors of the first paper said that "when type I error rate higher than 5.25 is considered conservative and lower than 4.75 is liberal" but to me it is the opposite (if I reject H0 when it is true more than I should I'd be being liberal, and if do it less than I should I'd be being conservative).

Idk if I'm missing something or if the authors made a mistake. But I need help understanding this.

The paper's doi is https://doi.org/10.5964/meth.11721

Bradley paper: https://doi.org/10.1111/j.2044-8317.1978.tb00581.x

Answer 1

I took a look at the paper (thanks for the link, btw), and started reading the first paragraph. In it, the authors state "ANOVA is a parametric test that depends on three distributional assumptions: (a) study groups scores must be independent; (b) distribution of each group scores must be normal (normality); (c) the variances of group scores must be equal or constant (homoscedasticity).".

Assumptions (b) and (c) are simply incorrect; it is not the marginal distributions which need to be normal, but the residuals, and homoscedasticity is not required, as there is a "Welch-flavor" of the ANOVA which dispenses of this assumption (see also here).

Let's just say that I stopped reading after that (a paper about ANOVA which can not get the basic assumptions behind ANOVA right...).

And yes, they have liberal vs. conservative backwards.

So your option that "the authors made a mistake" appears proven (and more than one mistake).