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False Positive Pregnancy Test First Response

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The term false discovery rate (FDR) was used by Colquhoun (2014) to mean the probability that a "significant" result was a false positive. Later Colquhoun (2017) used the term false positive risk (FPR) for the same quantity, to avoid confusion with the term FDR as used by people who work on multiple comparisons. Corrections for multiple comparisons aim only to correct the type I error rate, so the result is a (corrected) p value. Thus they are susceptible to the same misinterpretation as any other p value. The false positive risk is always higher, often much higher, than the p value. Confusion of these two ideas, the error of the transposed conditional, has caused much mischief. Because of the ambiguity of notation in this field, it is essential to look at the definition in every paper. The hazards of reliance on p-values was emphasized in Colquhoun (2017) by pointing out that even an observation of p = 0. 001 was not necessarily strong evidence against the null hypothesis. Despite the fact that the likelihood ratio in favor of the alternative hypothesis over the null is close to 100, if the hypothesis was implausible, with a prior probability of a real effect being 0. 1, even the observation of p = 0. 001 would have a false positive rate of 8 percent. It wouldn't even reach the 5 percent level. As a consequence, it has been recommended that every p value should be accompanied by the prior probability of there being a real effect that it would be necessary to assume in order to achieve a false positive risk of 5%. For example, if we observe p= 0. 05 in a single experiment, we would have to be 87% certain that there as a real effect before the experiment was done to achieve a false positive risk of 5%.

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