Question: If p has a uniform distribution in the range (0, 1) show that - 2 loge p has a X2-distribution with degrees of freedom 2. If there are k independent tests, b each with a p-value, then
has a X2 distribution with d.f. 2k. This statistic can be used for an overall rejection or acceptance of the null hypothesis based on the k independent tests. [See G. S. Maddala, Econometrics (New York: McGraw-Hill, 1977), p. 48. The test is from C. R. Rao, Advanced Statistical Methods in Biometric Research (New York: Wiley, 1952), p. 44.]