Fig. 1

Graphical representation of the method of estimation of the chances that a statistically significant result represents a “true–positive” based on 100 hypothetical trials where there is a 10% chance the hypothesis is correct and experiments are conducted with 90% power at an α of 0.05. In this example, where there is a 10% prior probability that the hypothesis is correct, each box represents a hypothetical trial. The top row of boxes (surrounded by a green line) represent the 10 occasions where the hypothesis is correct; the remaining 90 boxes represent the occasions where the null hypothesis is correct. In an experiment with 90% power, one would expect to correctly identify nine of ten correct hypotheses (the area shaded red). Because the α value is defined as the probability of rejecting the null hypothesis when the null hypothesis is correct, one would also expect to incorrectly reject the null hypothesis on 4.5 of 90 occasions (the area shaded blue). As a result, with a 10% prior probability in an experiment with 90% power, a true-positive result is expected 67% of the time when the P value is 0.05