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In a provocative article Ioannidis (2005) argues that, in disciplines employing statistical tests of significance, professional journals report more wrong than true significant results. This short note sketches the argument and explores under what conditions the assertion holds. The “positive predictive value” (PPV) is lower than 1/2 if the a priori probability of the truth of a hypothesis is low. However, computation of the PPV includes only significant results. If both significant and non-significant results are taken into account the “total error ratio” (TER) will not exceed 1/2 provided no extremely large publication bias is present. Moreover, it is shown that theory-driven research may reduce the proportion of errors. Also, the role of replications is emphasized; replication studies of original research are so important because they drastically decrease the error ratio.

Are Most Published Research Findings False?