A Graphical Aid for Determining Sample Size when Comparing Two Independent Proportions

Abstract

Standard sample size calculations for n, the number of observations per group when comparing two independent proportions, P1 and P2, require the specification of four quantities: P1, one of the two proportions of interest; delta = P2 - P1, the smallest difference which it is important to detect; alpha, the significance level; and beta, the chance of failing to detect a difference as large as delta. In terms of these four quantities, the graphical aid is a series of charts showing isographs of sample size for selected values of n ranging from 35 to 500. The isographs, i.e. curves connecting points of equal sample size, are based on the asymptotic arc sine approximation and are plotted on the grid formed by P1 on the abscissa and delta on the ordinate. Eight separate charts are available for different choices of alpha and beta. These charts are especially useful in situations where the feasible sample size is roughly known, in which case the detectable difference, delta, can be read directly from the graph.