Psychology journals rarely publish nonsignificant results. At the same time, it is often very unlikely (or "too good to be true") that a set of studies yields exclusively significant results. Here, we use likelihood ratios to explain when sets of studies that contain a mix of significant and nonsignificant results are likely to be true or "too true to be bad." As we show, mixed results are not only likely to be observed in lines of research but also, when observed, often provide evidence for the alternative hypothesis, given reasonable levels of statistical power and an adequately controlled low Type 1 error rate. Researchers should feel comfortable submitting such lines of research with an internal meta-analysis for publication. A better understanding of probabilities, accompanied by more realistic expectations of what real sets of studies look like, might be an important step in mitigating publication bias in the scientific literature.
Keywords: likelihoods; power; publication bias; statistical inferences.