On the tests of separate families of hypotheses with small sample size

It is often necessary in statistical methodology to test whether given observations follow one or the other of two possible probability distributions. If the statistical methods used are fairly robust, the theoretical distribution need not fit the data particularly well. In such cases, approximate methods may be adequate, and usually the X 2-goodness-of-tit test might be employed. However, it may sometimes be necessary to know which of two similardistributions fits a set of data better. More powerful tests are then required. Tests of separate families of hypotheses have been developed by Cox (1961, 1962) which employ the test statistic, which is assumed to follow a standard normal distribution when the hypothesis Hf is true. In this paper, one deals with this problem by using computer simulation when the sample size is small and calculates percentage points of the test statistic for 0.01, 0.05, 0.10, 0.90,0.95, 0.99.