The Reproducibility Of Research And The Misinterpretation Of P Values

Abstract

We wish to answer this question If you observe a \"significant\" P value after doing a single unbiased experiment, what is the probability that your result is a false positive?. The weak evidence provided by P values between 0.01 and 0.05 is explored by exact calculations of false positive rates.\n\nWhen you observe P = 0.05, the odds in favour of there being a real effect (given by the likelihood ratio) are about 3. This is far weaker evidence than the odds of 19 to 1 that might, wrongly, be inferred from the P value. And if you want to limit the false positive rate to 5 percent, you would have to assume that you were 87% sure that there was a real effect before the experiment was done.\n\nIf you observe P = 0.001, which gives likelihood ratio of 100:1 odds on there being a real effect, that would usually be regarded as conclusive, But the false positive rate would still be 8% if the prior probability of a real effect was only 0.1\n\nDespite decades of warnings, many areas of science still insist on labelling a result of P < 0.05 as \"significant\". This must account for a substantial part of the lack of reproducibility in some areas of science. And this is before you get to the many other well-known problems, like multiple comparisons, lack of randomisation and P-hacking. Science is endangered by statistical misunderstanding, and by people who impose perverse incentives on scientists.