What is Deborah Mayo's "severity"? Can anyone give a detailed (and clear) explanation of what her "severity" means (isn't it just the power function assessed at different discrepancies taken as null hypothesis?) and how it fits in the statistical testing literature in general?
 A: Yes the severity of a statistical claim C is always in relation to a test and an outcome. It's a measure of how well a claim's flaws are put to a test and found absent. A hypothesis  C severely passes a test with result x to the extent that a result that is more discordant from C than is x would probability have occurred were C false. Say that a null hypothesis is rejected in a one-sided Normal test of the mean with an outcome that just reaches the significance level of .025. The significant result indicates some discrepancy from the null, but there is a worry someone will make mountains out of molehills. Spoze the power against an alternative mu' is high. Then the severity for inferring mu> mu' is LOW. That's because the probability of observing a larger difference than observed is probable assuming mu' is true. So severity goes in the direction opposite of power when the data lead to a rejection of a null  My new book explains all this in clear detail: Statistical Inference as Severe Testing: How to Get beyond the Statistics Wars.
