# Article with differents means considered equals

In this study, the researcher wrote the following:

Atheists also retracted God statements equally often (M = 1.33, SD = 3.42) as did religious individuals (M = 2.92, SD = 4.50), F(1, 26) = 1.054, p = .314, η2 = 0.046.

Why is it that a mean of 1.33 would be considered "equally often" as a mean of 2.92? Am I missing something?

## 1 Answer

The author's statement is a mischaracterization of a failure to reject the null of equal population means.

The sample means are obviously different, but not so different as to be inconsistent with identical population means.

The failure to reject may have more to do with the small sample size (16 vs 13), since at small sample sizes even quite large differences in mean would lead to failure to reject. [I didn't notice any mention of a pre-sampling power calculation.]

[Additional caution should be exercised in interpreting this study because on a quick skim through (i.e. it's possible I missed something) it's not made clear how these samples were obtained, yet the study attempts to apply its conclusions very broadly (outside not only the samples, but even outside the population of the country the study was done in). Presumably (in the absence of any discussion of the effort in obtaining random samples) these samples would likely have been obtained via some form of convenience sampling.]