S-values in statistical inference

James Brophy writes about key issues in the statistical interpretation of RCTs in the Canadian Journal of Cardiology. What caught my eye was the mention about S-values:

Enhanced understanding of the strength of the evidence against not only the null hypothesis but against any specific alternative hypotheses can be more easily appreciated by considering p values not on their natural probability scale from 0 to 1 but on a scale that reflects the probability of successive tosses, s, of an unbiased coin showing only heads, p = (1/2)s.(10) This is known as the binary Shannon information, surprisal or S value which can be rearranged as s = log2(1/p) = −log2(p).

Reference 10 they cite is an excellent paper by Rafi & Greenland which gives very thorough insight how P-values should be interpreted as measures of compatibility and how P-values should be supplemented with quantitative-information concepts like S-values. Rafi & Greenland paper should be read by all clinical researchers!

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