On testing equality of means of correlated variables with incomplete data
Umesh D. Naik · Biometrika · 1975
Suppose that we have a sample from a bivariate normal population with variances σ12σ22 and correlation coefficient ρ, but some observations on one of the two variables are missing. Based on these data, we wish to test the hypothesis of equality of means of the two variables. In this paper, classes of test procedures are given for when the alternative is one-sided and for when it is two-sided. The tests satisfy the property that the probability of type I error does not exceed a preassigned level α when ρ is negative, and when ρ is positive but small. The test that is to be recommended in a particular situation depends on what information, if any, is available about the nuisance parameters. Comparisons of the tests with the paired t test and the Mehta & Gurland (1969, 1973) test are also included.