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.