Small Sample Exact Power of the Range from a Symmetric Multinomial Distribution

The authors (1968) have previously given tables of the percentage points of the range (= w ) of r samples from a multinomial distribution of r cells each with probability r −1 , r = 2(1)10. This paper presents the small sample power of w for r = 2(1)6 under alternatives H to the null hypothesis H 0 of a symmetric multinomial distribution. The alternatives are of the form H: p i =r −1 + c 1 n 1/2 i = 1, …, r , where the c 's are such that ∑ c i =0, i. e. H consists of a set of multinomial probabilities approaching H 0 of 0(n −1/2 ). Table 1 gives values of the power of the range test, and Table 2 consists of selected comparisons of the power with respect to the X 2 index of dispersion.