Some new methods for testing randomness of a binomial sequence and its applications in two sample problems

Abstract

The t-test commonly used for testing two samples is based on the assumption that the sample are random and belong to the same normal population. These assumptions may or may not be valid for different types of experimental data. In cases where these assumptions do not hold good, it would be preferable to use tests which are independent of the nature of the distribution of the parent population. A number of such tests, some developed in the Defence Science Laboratory, is given in this paper. The test depend on a sequence of A's and B's obtained by pooling together the two samples {Xm}and {Yn} and arranging them in ascending or descending order and treating the observations belonging to {xm} and {yn} as A's and B's respectively. For this sequence the number of AB's or AB's and BA's are noted for the following cases: (1) Between any two observations of the sequence separated by (k-1) observations or less; (2) Between any two observations in blocks of (k+1) consecutive observations moving from one end to the other end. It has been found that the standardized deviates of these statics serve as more reliable tests than any of other existing tests. Further work is in progress to confirm these findings.