No abstract

The designing, collecting, analyzing, and reporting of psychological studies entail many choices that are often arbitrary. The opportunistic use of these so-called researcher degrees of freedom aimed at obtaining statistically significant results is problematic because it enhances the chances of false positive results and may inflate effect size estimates. In this review article, we present an extensive list of 34 degrees of freedom that researchers have in formulating hypotheses, and in designing, running, analyzing, and reporting of psychological research. The list can be used in research methods education, and as a checklist to assess the quality of preregistrations and to determine the potential for bias due to (arbitrary) choices in unregistered studies.

We conducted preregistered replications of 28 classic and contemporary published findings, with protocols that were peer reviewed in advance, to examine variation in effect magnitudes across samples and settings. Each protocol was administered to approximately half of 125 samples that comprised 15,305 participants from 36 countries and territories. Using the conventional criterion of statistical significance ( p < .05), we found that 15 (54%) of the replications provided evidence of a statistically significant effect in the same direction as the original finding. With a strict significance criterion ( p < .0001), 14 (50%) of the replications still provided such evidence, a reflection of the extremely high-powered design. Seven (25%) of the replications yielded effect sizes larger than the original ones, and 21 (75%) yielded effect sizes smaller than the original ones. The median comparable Cohen’s ds were 0.60 for the original findings and 0.15 for the replications. The effect sizes were small (< 0.20) in 16 of the replications (57%), and 9 effects (32%) were in the direction opposite the direction of the original effect. Across settings, the Q statistic indicated significant heterogeneity in 11 (39%) of the replication effects, and most of those were among the findings with the largest overall effect sizes; only 1 effect that was near zero in the aggregate showed significant heterogeneity according to this measure. Only 1 effect had a tau value greater than .20, an indication of moderate heterogeneity. Eight others had tau values near or slightly above .10, an indication of slight heterogeneity. Moderation tests indicated that very little heterogeneity was attributable to the order in which the tasks were performed or whether the tasks were administered in lab versus online. Exploratory comparisons revealed little heterogeneity between Western, educated, industrialized, rich, and democratic (WEIRD) cultures and less WEIRD cultures (i.e., cultures with relatively high and low WEIRDness scores, respectively). Cumulatively, variability in the observed effect sizes was attributable more to the effect being studied than to the sample or setting in which it was studied.

This study documents reporting errors in a sample of over 250,000 p-values reported in eight major psychology journals from 1985 until 2013, using the new R package “statcheck.” statcheck retrieved null-hypothesis significance testing (NHST) results from over half of the articles from this period. In line with earlier research, we found that half of all published psychology papers that use NHST contained at least one p-value that was inconsistent with its test statistic and degrees of freedom. One in eight papers contained a grossly inconsistent p-value that may have affected the statistical conclusion. In contrast to earlier findings, we found that the average prevalence of inconsistent p-values has been stable over the years or has declined. The prevalence of gross inconsistencies was higher in p-values reported as significant than in p-values reported as nonsignificant. This could indicate a systematic bias in favor of significant results. Possible solutions for the high prevalence of reporting inconsistencies could be to encourage sharing data, to let co-authors check results in a so-called “co-pilot model,” and to use statcheck to flag possible inconsistencies in one’s own manuscript or during the review process.

Publication bias threatens the validity of meta-analytic results and leads to overestimation of the effect size in traditional meta-analysis. This particularly applies to meta-analyses that feature small studies, which are ubiquitous in psychology. Here we develop a new method for meta-analysis that deals with publication bias. This method, p-uniform, enables (a) testing of publication bias, (b) effect size estimation, and (c) testing of the null-hypothesis of no effect. No current method for meta-analysis possesses all 3 qualities. Application of p-uniform is straightforward because no additional data on missing studies are needed and no sophisticated assumptions or choices need to be made before applying it. Simulations show that p-uniform generally outperforms the trim-and-fill method and the test of excess significance (TES; Ioannidis & Trikalinos, 2007b) if publication bias exists and population effect size is homogenous or heterogeneity is slight. For illustration, p-uniform and other publication bias analyses are applied to the meta-analysis of McCall and Carriger (1993) examining the association between infants' habituation to a stimulus and their later cognitive ability (IQ). We conclude that p-uniform is a valuable technique for examining publication bias and estimating population effects in fixed-effect meta-analyses, and as sensitivity analysis to draw inferences about publication bias.