The following procedure is suggested "Consider whether one of the simplest methods of analysis (equal weights, equal weights within treatments, equal weights within replicates) can be used without further investigation. If in doubt apply the appropriate test. If none of the methods in [the above] appears satisfactory, estimate the relative amounts of binomial and extraneous variation from an analysis of variance of the fractions or percentages." Examples are selected for the paper from the services and conceptions of 6 bulls in artificial insemination tests. The more closely the weighted numbers approach the true weights, the smaller is the disturbance of the z, F, and t values in levels of significance.