  During multiple testing, researchers often adjust their alpha level to
control the familywise error rate for a statistical inference about a joint
union alternative hypothesis (e.g., "H1,1 or H1,2"). However, in some cases,
they do not make this inference. Instead, they make separate inferences about
each of the individual hypotheses that comprise the joint hypothesis (e.g.,
H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to
adjust their alpha level from the conventional level of 0.050 to 0.025 when
testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not
for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However,
these separate individual inferences do not require an alpha adjustment. Only a
statistical inference about the union alternative hypothesis "H1,1 or H1,2"
requires an alpha adjustment because it is based on "at least one" significant
result among the two tests, and so it refers to the familywise error rate.
Hence, an inconsistent correction occurs when a researcher corrects their alpha
level during multiple testing but does not make an inference about a union
alternative hypothesis. In the present article, I discuss this inconsistent
correction problem, including its reduction in statistical power for tests of
individual hypotheses and its potential causes vis-a-vis error rate confusions
and the alpha adjustment ritual. I also provide three illustrations of
inconsistent corrections from recent psychology studies. I conclude that
inconsistent corrections represent a symptom of statisticism, and I call for a
more nuanced inference-based approach to multiple testing corrections.
