A central assumption of meta-analysis is that the sample of studies fairly represents all work done in the field, published and unpublished. However, if studies with "poor" results are less likely to be published, a potential publication bias is present. The authors propose a maximum likelihood approach to estimating publication bias for the situation in which censorship based on effect size may occur. An explicit hypothesis test is provided for testing whether or not censorship is present. The method also simultaneously estimates the proportion of studies censored, the threshold past which censorship is avoided, and the probability of censorship if a potential observation is under the censorship threshold. Two published meta-analyses are examined and some publication bias is found in each, but no publication bias is detected in a meta-analysis of proprietary research data.
Rust, Roland, Donald Lehmann, and John Farley. "Estimating Publication Bias in Meta-analysis." Journal of Marketing Research 27, no. 2 (May 1990): 220-26.
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