The article with the witty title “Do Studies of Statistical Power Have an Effect on the Power of Studies?” builds on Cohen’s (1962) seminal power analysis of psychological research.

The main point of the article can be summarized in one word: No. Statistical power has not increased after Cohen published his finding that statistical power is low.

One important contribution of the article was a meta-analysis of power analyses that applied Cohen’s method to a variety of different journals. The table below shows that power estimates vary by journal assuming that the effect size was medium according to Cohen’s criteria of small, medium, and large effect sizes. The studies are sorted by power estimates from the highest to the lowest value, which provides a power ranking of journals based on Cohen’s method. I also included the results of Sedlmeier and Giegerenzer’s power analysis of the 1984 volume of the Journal of Abnormal Psychology (the Journal of Social and Abnormal Psychology was split into Journal of Abnormal Psychology and Journal of Personality and Social Psychology). I used the mean power (50%) rather than median power (44%) because the mean power is consistent with the predicted success rate in the limit. In contrast, the median will underestimate the success rate in a set of studies with heterogeneous effect sizes.

The table shows that there is tremendous variability in power estimates for different journals ranging from as high as 89% (9 out of 10 studies will produce a significant result when an effect is present) to the lowest estimate of  37% power (only 1 out of 3 studies will produce a significant result when an effect is present).

The table also shows that the Journal of Abnormal and Social Psychology and its successor the Journal of Abnormal Psychology yielded nearly identical power estimates. This finding is the key finding that provides empirical support for the claim that power in the Journal of Abnormal Psychology has not increased over time.

The average power estimate for all journals in the table is 62% (median 61%).  The list of journals is not a representative set of journals and few journals are core psychology journals. Thus, the average power may be different if a representative set of journals had been used.

The average for the three core psychology journals (JASP & JAbnPsy,  JAP, AJEduPsy) is 67% (median = 63%) is slightly higher. The latter estimate is likely to be closer to the typical power in psychology in general rather than the prominently featured estimates based on the Journal of Abnormal Psychology. Power could be lower in this journal because it is more difficult to recruit patients with a specific disorder than participants from undergraduate classes. However, only more rigorous studies of power for a broader range of journals and more years can provide more conclusive answers about the typical power of a single statistical test in a psychology journal.

The article also contains some important theoretical discussions about the importance of power in psychological research. One important issue concerns the treatment of multiple comparisons. For example, a multi-factorial design produces an exponential number of statistical comparisons. With two conditions, there is only one comparison. With three conditions, there are three comparisons (C1 vs. C2, C1 vs. C3, and C2 vs. C3). With 5 conditions, there are 10 comparisons. Standard statistical methods often correct for these multiple comparisons. One consequence of this correction for multiple comparisons is that the power of each statistical test decreases. An effect that would be significant in a simple comparison of two conditions would not be significant if this test is part of a series of tests.

Sedlmeier and Giegerenzer used the standard criterion of p < .05 (two-tailed) for their main power analysis and for the comparison with Cohen’s results. However, many articles presented results using a more stringent criterion of significance. If the criterion used by authors would have been used for the power analysis, power decreased further. About 50% of all articles used an adjusted criterion value and if the adjusted criterion value was used power was only 37%.

Sedlmeier and Giegerenzer also found another remarkable difference between articles in 1960 and in 1984. Most articles in 1960 reported the results of a single study. In 1984 many articles reported results from two or more studies. Sedlmeier and Giegerenzer do not discuss the statistical implications of this change in publication practices. Schimmack (2012) introduced the concept of total power to highlight the problem of publishing articles that contain multiple studies with modest power. If studies are used to provide empirical support for an effect, studies have to show a significant effect. For example, Study 1 shows an effect with female participants. Study 2 examines whether the effect can also be demonstrated with male participants. If Study 2 produces a non-significant result, it is not clear how this finding should be interpreted. It may show that the effect does not exist for men. It may show that the first result was just a fluke finding due to sampling error. Or it may show that the effect exists equally for men and women but studies had only 50% power to produce a significant result. In this case, it is expected that one study will produce a significant result and one will produce a non-significant result, but in the long-run significant results are equally likely with male or female participants. Given the difficulty of interpreting a non-significant result, it would be important to conduct a more powerful study that examines gender differences in a more powerful study with more female and male participants. However, this is not what researchers do. Rather, multiple study articles contain only the studies that produced significant results. The rate of successful studies in psychology journals is over 90% (Sterling et al., 1995). However, this outcome is extremely likely in multiple studies where studies have only 50% power to get a significant result in a single attempt. For each additional attempt, the probability to obtain only significant results decreases exponentially (1 Study, 50%, 2 Studies 25%, 3 Studies 12.5%, 4 Studies 6.75%).

The fact that researchers only publish studies that worked is well-known in the research community. Many researchers believe that this is an acceptable scientific practice. However, consumers of scientific research may have a different opinion about this practice. Publishing only studies that produced the desired outcome is akin to a fund manager that only publishes the return rate of funds that gained money and excludes funds with losses. Would you trust this manager to take care of your retirement? It is also akin to a gambler that only remembers winnings. Would you marry a gambler who believes that gambling is ok because you can earn money that way?

I personally do not trust obviously biased information. So, when researchers present 5 studies with significant results, I wonder whether they really had the statistical power to produce these results or whether they simply did not publish results that failed to confirm their claims. To answer this question it is essential to estimate the actual power of individual studies to produce significant results; that is, it is necessary to estimate the typical power in this field, of this researcher, or in the journal that published the results.

In conclusion, Sedlmeier and Gigerenzer made an important contribution to the literature by providing the first power-ranking of scientific journals and the first temporal analyses of time trends in power. Although they probably hoped that their scientific study of power would lead to an increase in statistical power, the general consensus is that their article failed to change scientific practices in psychology. In fact, some journals required more and more studies as evidence for an effect (some articles contain 9 studies) without any indication that researchers increased power to ensure that their studies could actually provide significant results for their hypotheses. Moreover, the topic of statistical power remained neglected in the training of future psychologists.

I recommend Sedlmeier and Gigerenzer’s article as essential reading for anybody interested in improving the credibility of psychology as a rigorous empirical science.

As always, comments (positive or negative) are always welcome.