Post provided by JARROD HADFIELD
Last week the Center for Open Science held a meeting with the aim of improving inference in ecology and evolution. The organisers (Tim Parker, Jessica Gurevitch & Shinichi Nakagawa) brought together the Editors-in-chief of many journals to try to build a consensus on how improvements could be made. I was brought in due to my interest in statistics and type I errors – be warned, my summary of the meeting is unlikely to be 100% objective.
True Positives and False Positives
The majority of findings in psychology and cancer biology cannot be replicated in repeat experiments. As evolutionary ecologists we might be tempted to dismiss this because psychology is often seen as a “soft science” that lacks rigour and cancer biologists are competitive and unscrupulous. Luckily, we as evolutionary biologists and ecologists have that perfect blend of intellect and integrity. This argument is wrong for an obvious reason and a not so obvious reason.
We tend to concentrate on significant findings, and with good reason: a true positive is usually more informative than a true negative. However, of all the published positives what fraction are true positives rather than false positives? The knee-jerk response to this question is 95%. However, the probability of a false positive (the significance threshold, alpha) is usually set to 0.05, and the probability of a true positive (the power, beta) in ecological studies is generally less than 0.5 for moderate sized effects. The probability that a published positive is true is therefore 0.5/(0.5+0.05) =91%. Not so bad. But, this assumes that the hypotheses and the null hypothesis are equally likely. If that were true, rejecting the null would give us very little information about the world (a single bit actually) and is unlikely to be published in a widely read journal. A hypothesis that had a plausibility of 1 in 25 prior to testing would, if true, be more informative, but then the true positive rate would be down to (1/25)*0.5/((1/25)*0.5+(24/25)*0.05) =29%. So we can see that high false positive rates aren’t always the result of sloppiness or misplaced ambition, but an inevitable consequence of doing interesting science with a rather lenient significance threshold. Continue reading