Combining the Probabilities from Significance Tests

Abstract

THE statistic Q proposed by van Valen1 is such that, under the null hypothesis, 2 log 1/2Q is distributed as the modulus of the difference of two independent χ2 variables each of 2N degrees of freedom (where N = n + m in van Valen's notation). It follows that the use of Q as ‘the combined probability desired’ is not correct without a functional transformation: namely, using the result of David et al.2 for the distribution of the difference of two χ2 variables, the value: should be used, where: (Km(z) being a standard notation for the modified Bessel function of second kind with imaginary argument).