Scientists often adjust their significance threshold during null hypothesis significance testing in order to take into account multiple testing and multiple comparisons. This alpha adjustment has become particularly relevant in the context of the replication crisis in science. The present article considers the conditions in which this alpha adjustment is appropriate and the conditions in which it is inappropriate. A distinction is drawn between three types of multiple testing: disjunction testing, conjunction testing, and individual testing. It is argued that alpha (...) adjustment is only appropriate in the case of disjunction testing, in which at least one test result must be significant in order to reject the associated joint null hypothesis. Alpha adjustment is inappropriate in the case of conjunction testing, in which all relevant results must be significant in order to reject the joint null hypothesis. Alpha adjustment is also inappropriate in the case of individual testing, in which each individual result must be significant in order to reject each associated individual null hypothesis. The conditions under which each of these three types of multiple testing is warranted are examined. It is concluded that researchers should not automatically assume that alpha adjustment is necessary during multiple testing. Illustrations are provided in relation to joint studywise hypotheses and joint multiway ANOVAwise hypotheses. (shrink)

Fisher criticised the Neyman-Pearson approach to hypothesis testing by arguing that it relies on the assumption of “repeated sampling from the same population.” The present article considers the responses to this criticism provided by Pearson and Neyman. Pearson interpreted alpha levels in relation to imaginary replications of the original test. This interpretation is appropriate when test users are sure that their replications will be equivalent to one another. However, by definition, scientific researchers do not possess sufficient knowledge about the relevant (...) and irrelevant aspects of their tests and populations to be sure that their replications will be equivalent to one another. Pearson also interpreted the alpha level as a personal rule that guides researchers’ behavior during hypothesis testing. However, this interpretation fails to acknowledge that the same researcher may use different alpha levels in different testing situations. Addressing this problem, Neyman proposed that the average alpha level adopted by a particular researcher can be viewed as an indicator of that researcher’s typical Type I error rate. Researchers’ average alpha levels may be informative from a metascientific perspective. However, they are not useful from a scientific perspective. Scientists are more concerned with the error rates of specific tests of specific hypotheses, rather than the error rates of their colleagues. It is concluded that neither Neyman nor Pearson adequately rebutted Fisher’s “repeated sampling” criticism. Fisher’s significance testing approach is briefly considered as an alternative to the Neyman-Pearson approach. (shrink)

Metascientists have studied questionable research practices in science. The present article considers the parallel concept of questionable metascience practices (QMPs). A QMP is a research practice, assumption, or perspective that has been questioned by several commentators as being potentially problematic for metascience and/or the science reform movement. The present article reviews ten QMPs that relate to criticism, replication, bias, generalization, and the characterization of science. Specifically, the following QMPs are considered: (1) rejecting or ignoring self-criticism; (2) a fast ‘n’ bropen (...) scientific criticism style; (3) overplaying the role of replication in science; (4) assuming a replication rate is “too low” without specifying an “acceptable” rate; (5) an unacknowledged metabias towards explaining the replication crisis in terms of researcher bias; (6) assuming that researcher bias can be reduced; (7) devaluing exploratory results as being more “tentative” than confirmatory results; (8) presuming that questionable research practices are problematic research practices; (9) focusing on knowledge accumulation; and (10) focusing on specific scientific methods. It is stressed that only some metascientists engage in some QMPs some of the time, and that these QMPs may not always be problematic. Research is required to estimate the prevalence and impact of QMPs. In the meantime, QMPs should be viewed as invitations to ask questions about how we go about doing better metascience. (shrink)