中華心理學刊
民9 7 ， 5 0 卷， 1 期， 2 1 - 2 9

Peter H. Schonemann（Department of Psychology, Purdue University）；Jeffrey D. Scargle（Space Science Division, NASA Ames Research Center）

Abstract

Scargle (2000) has discussed Rosenthal and Rubin's (1978) fail-safe number" (FSN) method for estimating the number of unpublished studies in meta-analysis. He concluded that this FSN cannot possibly be correct because a central assumption the authors used conflicts with the very definition of publication bias. While this point has been made by others before (Darlington, 1980; Elsahoff, 1978; Iyengar & Greenhouse, 1988; Thomas, 1985), Scargle showed, by way of a simple 2-parameter model, how far off Rosenthal and Rubin, s estimate can be in practice. However, his results relied on the assumption that the decision variable is normally distributed with zero mean. In this case the ratio of unpublished to published papers is large only in a tiny region of the parameter plane. Building on these results, we now show that (1) replacing densities with probability masses greatly simplifies Scargle's derivations and permits an explicit statement of the relation between the probability α of Type I errors and the step-size β; (2) this result does not require any distribution assumptions; (3) the distinction between 1-sided and 2-sided rejection regions becomes immaterial; (4) this distribution-free approach leads to an immediate generalization to partitions involving more than two intervals, and thus covers more general selection functions.

Keywords: publication bias, meta-analysis, file-drawer hypothesis, fail-safe number