A New Method for Testing Two Binomial Samples with its Application in Statistical Quality Control

Abstract

A new method for comparing the proportions observed in two binomial samples involved the characters, say A and B with probabilities p & q has been given in this paper. This method provides the basis for a more reliable comparison than the usual 2X2x/sup/2-contingency test. Taking the samples in order of occurrence to be x1,x2,x3....xn; y1,y2,....yn, the tests depend on the statics Xs and Ys which are based on a system of scoring sigma(xk-y1) or sigma|xk-y1| where |k-l|<=s, a constant. The score for (xk-y1) is zero for combination AA or BB and is+1 or-1 if the combination is AB or BA. Similarly |xk-Y1| is zero in the first case and +1 in the latter two cases. The tests have been illustrated for examining the percentage of defectives produced in two machines. The applications of the tests in psychological investigation have also been explained with reference to the data discussed by McNemar.