400: A Method for Combining Non-Independent, One-Sided Tests of Significance

Littell and Folks .1971, 1973 show that Fisher's method of combining independenlt tests of significance is asymptotically optimal among essentially all methods of combining independent tests. By assuming a joint multivariate normal density for the variables, we approximate the distribultion of Fisher's statistic in order to combiine one-sided tests of location when all the variables are not jointly inidependent. The probability associated with this test is simpler to evaluate than that of the equivalent likelihood ratio test.