Mark Rubin

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-à-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.

The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin with an introduction to Type I error rates that distinguishes them from theoretical errors. I then illustrate my argument with respect to model misspecification, multiple testing, selective inference, forking paths, exploratory analyses, p-hacking, optional stopping, double dipping, and HARKing. In each case, I demonstrate that relevant Type I error rates are not usually inflated above their nominal level, and in the rare cases that they are, the inflation is easily identified and resolved. I conclude that the replication crisis may be explained, at least in part, by researchers’ misinterpretation of statistical errors and their underestimation of theoretical errors.

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.

Popper’s (1983, 2002) philosophy of science has enjoyed something of a renaissance in the wake of the replication crisis, offering a philosophical basis for the ensuing science reform movement. However, adherence to Popper’s approach may also be at least partly responsible for the sense of “crisis” that has developed following multiple unexpected replication failures. In this article, I contrast Popper’s approach with Lakatos’ (1978) approach and a related approach called naïve methodological falsificationism (NMF; Lakatos, 1978). The Popperian approach is powerful because it is based on logical refutation, but its theories are noncausal and, therefore, lacking in scientific value. In contrast, the Lakatosian approach considers causal theories, but it concedes that these theories are not logically refutable. Finally, the NMF approach subjects Lakatosian causal theories to Popperian logical refutations. However, its approach of temporarily accepting a ceteris paribus clause during theory testing may be viewed as scientifically inappropriate, epistemically inconsistent, and “completely redundant” (Lakatos, 1978, p. 40). I conclude that the replication “crisis” makes the most sense in the context of the Popperian and NMF approaches because it is only in these two approaches that replication failures represent logical refutations of theories. In contrast, replication failures are less problematic in the Lakatosian approach because they do not logically refute theories. Indeed, in the Lakatosian approach, replication failures can be legitimately ignored or used to motivate theory development.

Preregistration has been proposed as a useful method for making a publicly verifiable distinction between confirmatory hypothesis tests, which involve planned tests of ante hoc hypotheses, and exploratory hypothesis tests, which involve unplanned tests of post hoc hypotheses. This distinction is thought to be important because it has been proposed that confirmatory hypothesis tests provide more compelling results (less uncertain, less tentative, less open to bias) than exploratory hypothesis tests. In this article, we challenge this proposition and argue that there are several advantages of exploratory hypothesis tests that can make their results more compelling than those of confirmatory hypothesis tests. We also consider some potential disadvantages of exploratory hypothesis tests and conclude that their advantages can outweigh the disadvantages. We conclude that exploratory hypothesis tests avoid researcher commitment and researcher prophecy biases, reduce the probability of data fraud, are more appropriate in the context of unplanned deviations, facilitate inference to the best explanation, and allow peer reviewers to make additional contributions at the data analysis stage. In contrast, confirmatory hypothesis tests may lead to an inappropriate level of confidence in research conclusions, less appropriate analyses in the context of unplanned deviations, and greater bias and errors in theoretical inferences.

Why do voters seek to change the political landscape or to retain it? System justification theory proposes that a separate system motive to preserve the existing order drives support for the status-quo, and that this motivation operates independently from personal and collective interests. But how does this explanation apply to recent populist shifts in the political order such as Brexit and the emergence of Donald Trump? While the system motive may seem useful in understanding why the usual progressives may want to stick with an established order, it seems insufficient to explain why the more conservative voters would want to upend the establishment. Thus, we compared SJT’s system motive explanation for the system attitudes of voters on both sides of the political divide to an alternative explanation drawn from the newer social identity model of system attitudes. According to SIMSA, the difficulty in explaining the system attitudes of Brexit/Trump and Remain/Clinton voters from SJT’s system motive standpoint can be resolved by focusing instead on the collective interests that both camps seek to satisfy with their votes. We examined these explanations in two studies conducted soon after Brexit and Trump’s election in 2016, with results providing more support for SIMSA than for SJT.

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.

This research draws from three distinct lines of research on the link between emotions and intergroup bias as springboard to integrative, new hypotheses. Past research suggests that emotions extrinsic to the outgroup (or “incidental”), and intrinsic to the outgroup (or “integral”), produce valence-congruent effects on intergroup bias when relevant or “applicable” to the outgroup (e.g., incidental/integral anger and ethnic outgroups). These emotions produce valenceincongruent effects when irrelevant or “non-applicable” to the outgroup (e.g., incidental/integral sadness and happiness, and ethnic outgroups). Internally valid and ecologically sound tests of these contrasting effects are missing; hence we examined them experimentally in meaningful settings of interethnic contact. To this end, we hybridized established research paradigms in mood and intergroup contact research; this approach enabled us to use same materials and induction methods to instigate incidental and integral emotions in a single research design. In Experiment 1, White Australian students (N= 93) inin vivoreal face-to-face contact with an ethnic tutor in their classroom displayed less interethnic bias when incidentally sad (vs. happy) or integrally happy (vs. sad). In Experiment 2, White American males' (N= 492) anti-Arab bias displayed divergent effects under incidental vs. integral (non-applicable) sadness/happiness and similar effects under incidental vs. integral (applicable) anger. The role of perceptions of agency in the emotion-inducing situation is also explored, tested, and explained drawing from mainstream emotion theory. As expected, integral and incidentalapplicableemotions caused valence congruent effects, at the opposite sides of the subjective agency spectrum, by encouraging the generalization of dislike from the outgroup contact partner to the outgroup as a whole. On the other hand, incidental-non-applicable emotions caused valence-incongruent effects on bias, under high agency conditions, by encouraging (non-partner-centered) heuristic processing. Because of the improved methodology, these effects can be regarded as genuine and not the byproduct of methodological artifacts. This theory-driven and empirically sound analysis of the interplay between emotion source, emotion applicability and subjective agency in intergroup contact can increase the precision of emotion-based bias reduction strategies by deepening understanding of the emotion conditions that lead to intergroup bias attenuation vs. exacerbation.

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.

The replication crisis has caused researchers to distinguish between exact replications, which duplicate all aspects of a study that could potentially affect the results, and direct replications, which duplicate only those aspects of the study that are thought to be theoretically essential to reproduce the original effect. The replication crisis has also prompted researchers to think more carefully about the possibility of making Type I errors when rejecting null hypotheses. In this context, the present article considers the utility of two types of Type I error probability: the Neyman–Pearson long run Type I error rate and the Fisherian sample-specific Type I error probability. It is argued that the Neyman–Pearson Type I error rate is inapplicable in social science because it refers to a long run of exact replications, and social science deals with irreversible units that make exact replications impossible. Instead, the Fisherian sample-specific Type I error probability is recommended as a more meaningful way to conceptualize false positive results in social science because it can be applied to each sample-specific decision about rejecting the same substantive null hypothesis in a series of direct replications. It is concluded that the replication crisis may be partly due to researchers’ unrealistic expectations about replicability based on their consideration of the Neyman–Pearson Type I error rate across a long run of exact replications.

Hypothesizing after the results are known, or HARKing, occurs when researchers check their research results and then add or remove hypotheses on the basis of those results without acknowledging this process in their research report (Kerr, 1998). In the present article, I discuss three forms of HARKing: (1) using current results to construct post hoc hypotheses that are then reported as if they were a priori hypotheses; (2) retrieving hypotheses from a post hoc literature search and reporting them as a priori hypotheses; and (3) failing to report a priori hypotheses that are unsupported by the current results. These three types of HARKing are often characterized as being bad for science and a potential cause of the current replication crisis. In the present article, I use insights from the philosophy of science to present a more nuanced view. Specifically, I identify the conditions under which each of these three types of HARKing is most and least likely to be bad for science. I conclude with a brief discussion about the ethics of each type of HARKing.

Several researchers have recently argued that p values lose their meaning in exploratory analyses due to an unknown inflation of the alpha level (e.g., Nosek & Lakens, 2014; Wagenmakers, 2016). For this argument to be tenable, the familywise error rate must be defined in relation to the number of hypotheses that are tested in the same study or article. Under this conceptualization, the familywise error rate is usually unknowable in exploratory analyses because it is usually unclear how many hypotheses have been tested on a spontaneous basis and then omitted from the final research report. In the present article, I argue that it is inappropriate to conceptualize the familywise error rate in relation to the number of hypotheses that are tested. Instead, it is more appropriate to conceptualize familywise error in relation to the number of different tests that are conducted on the same null hypothesis in the same study. Under this conceptualization, alpha level adjustments in exploratory analyses are (a) less necessary and (b) objectively verifiable. As a result, p values do not lose their meaning in exploratory analyses.

Gelman and Loken (2013, 2014) proposed that when researchers base their statistical analyses on the idiosyncratic characteristics of a specific sample (e.g., a nonlinear transformation of a variable because it is skewed), they open up alternative analysis paths in potential replications of their study that are based on different samples (i.e., no transformation of the variable because it is not skewed). These alternative analysis paths count as additional (multiple) tests and, consequently, they increase the probability of making a Type I error during hypothesis testing. The present article considers this forking paths problem and evaluates four potential solutions that might be used in psychology and other fields: (a) adjusting the prespecified alpha level, (b) preregistration, (c) sensitivity analyses, and (d) abandoning the Neyman-Pearson approach. It is concluded that although preregistration and sensitivity analyses are effective solutions to p-hacking, they are ineffective against result-neutral forking paths, such as those caused by transforming data. Conversely, although adjusting the alpha level cannot address p-hacking, it can be effective for result-neutral forking paths. Finally, abandoning the Neyman-Pearson approach represents a further solution to the forking paths problem.

Kerr coined the term ‘HARKing’ to refer to the practice of ‘hypothesizing after the results are known’. This questionable research practice has received increased attention in recent years because it is thought to have contributed to low replication rates in science. The present article discusses the concept of HARKing from a philosophical standpoint and then undertakes a critical review of Kerr’s twelve potential costs of HARKing. It is argued that these potential costs are either misconceived, misattributed to HARKing, lacking evidence, or that they do not take into account pre- and post-publication peer review and public availability to research materials and data. It is concluded that it is premature to conclude that HARKing has led to low replication rates.