@article {Colquhoun144337,
author = {Colquhoun, David},
title = {The Reproducibility Of Research And The Misinterpretation Of P Values},
year = {2017},
doi = {10.1101/144337},
publisher = {Cold Spring Harbor Laboratory},
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 risks. When you observe P = 0.05, the odds in favour of there being a real effect (given by the likelihood ratio) are about 3:1. 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 risk to 5 \%, you would have to assume that you were 87\% sure that there was a real effect before the experiment was done. If you observe P = 0.001 in a well-powered experiment, it gives a likelihood ratio of almost 100:1 odds on there being a real effect. That would usually be regarded as conclusive, But the false positive risk would still be 8\% if the prior probability of a real effect was only 0.1. And, in this case, if you wanted to achieve a false positive risk of 5\% you would need to observe P = 0.00045. It is recommended that the terms "significant" and "non-significant" should never be used. Rather, P values should be supplemented by specifying the prior probability that would be needed to produce a specified (e.g. 5\%) false positive risk. It may also be helpful to specify the minimum false positive risk associated with the observed P value. Despite decades of warnings, many areas of science still insist on labelling a result of P \< 0.05 as "significant". This practice 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 university presidents and research funders who impose perverse incentives on scientists.},
URL = {https://www.biorxiv.org/content/early/2017/08/07/144337},
eprint = {https://www.biorxiv.org/content/early/2017/08/07/144337.full.pdf},
journal = {bioRxiv}
}