Publication bias in psychology: A closer look at the correlation between sample size and effect size.

Previously observed negative correlations between sample size and effect size (n-ES correlation) in psychological research have been interpreted as evidence for publication bias and related undesirable biases. Here, we present two studies aimed at better understanding to what extent negative n-ES correlations reflect such biases or might be explained by unproblematic adjustments of sample size to expected effect sizes. In Study 1, we analysed n-ES correlations in 150 meta-analyses from cognitive, organizational, and social psychology and in 57 multiple replications, which are free from relevant biases. In Study 2, we used a random sample of 160 psychology papers to compare the n-ES correlation for effects that are central to these papers and effects selected at random from these papers. n-ES correlations proved inconspicuous in meta-analyses. In line with previous research, they do not suggest that publication bias and related biases have a strong impact on meta-analyses in psychology. A much higher n-ES correlation emerged for publications' focal effects. To what extent this should be attributed to publication bias and related biases remains unclear.

Heterogeneity estimates in a biased world.

Meta-analyses typically quantify heterogeneity of results, thus providing information about the consistency of the investigated effect across studies. Numerous heterogeneity estimators have been devised. Past evaluations of their performance typically presumed lack of bias in the set of studies being meta-analysed, which is often unrealistic. The present study used computer simulations to evaluate five heterogeneity estimators under a range of research conditions broadly representative of meta-analyses in psychology, with the aim to assess the impact of biases in sets of primary studies on estimates of both mean effect size and heterogeneity in meta-analyses of continuous outcome measures. To this end, six orthogonal design factors were manipulated: Strength of publication bias; 1-tailed vs. 2-tailed publication bias; prevalence of p-hacking; true heterogeneity of the effect studied; true average size of the studied effect; and number of studies per meta-analysis. Our results showed that biases in sets of primary studies caused much greater problems for the estimation of effect size than for the estimation of heterogeneity. For the latter, estimation bias remained small or moderate under most circumstances. Effect size estimations remained virtually unaffected by the choice of heterogeneity estimator. For heterogeneity estimates, however, relevant differences emerged. For unbiased primary studies, the REML estimator and (to a lesser extent) the Paule-Mandel performed well in terms of bias and variance. In biased sets of primary studies however, the Paule-Mandel estimator performed poorly, whereas the DerSimonian-Laird estimator and (to a slightly lesser extent) the REML estimator performed well. The complexity of results notwithstanding, we suggest that the REML estimator remains a good choice for meta-analyses of continuous outcome measures across varied circumstances.

Heterogeneity of Research Results: A New Perspective From Which to Assess and Promote Progress in Psychological Science.

Heterogeneity emerges when multiple close or conceptual replications on the same subject produce results that vary more than expected from the sampling error. Here we argue that unexplained heterogeneity reflects a lack of coherence between the concepts applied and data observed and therefore a lack of understanding of the subject matter. Typical levels of heterogeneity thus offer a useful but neglected perspective on the levels of understanding achieved in psychological science. Focusing on continuous outcome variables, we surveyed heterogeneity in 150 meta-analyses from cognitive, organizational, and social psychology and 57 multiple close replications. Heterogeneity proved to be very high in meta-analyses, with powerful moderators being conspicuously absent. Population effects in the average meta-analysis vary from small to very large for reasons that are typically not understood. In contrast, heterogeneity was moderate in close replications. A newly identified relationship between heterogeneity and effect size allowed us to make predictions about expected heterogeneity levels. We discuss important implications for the formulation and evaluation of theories in psychology. On the basis of insights from the history and philosophy of science, we argue that the reduction of heterogeneity is important for progress in psychology and its practical applications, and we suggest changes to our collective research practice toward this end.