Abstract This paper addresses the problem of estimating a binomial proportion from several independent samples in agricultural research, where the arithmetic average is widely used. The penalties of using a suboptimal estimator, the arithmetic estimator, relative to the preferred best estimator, the weighted average, are theoretically and empirically investigated, using numerical illustrations and simulation studies. Raw count data from a study of the proportion of inoculated transgenic hairy roots expressing resistance to cyst nematode in soybean (Glycine max) cultivars and a set of 10 examples of proportion estimation involving several independent samples are used for a practical evaluation of the findings. Results show that using the arithmetic average estimator can inflate variance and widen large sample confidence intervals of the estimates. The weighted average is recommended.
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