Estimation of effect size is of interest in many applied fields such as Psychology, Sociology and Education. However there are few nonparametric estimators of effect size proposed in the existing literature, and little is known about the distributional characteristics of these estimators. In this article, two estimators based on the sample quantiles are proposed and studied. The first one is the estimator suggested by Hedges and Olkin (see page 93 of Hedges & Olkin, 1985) for the situation where a treatment effect is evaluated against a control group (Case A). A modified version of the robust estimator by Hedges and Olkin is also proposed for the situation where two parallel treatments are compared (Case B). Large sample distributions of both estimators are derived. Their asymptotic relative efficiencies with respect to the normal maximum likelihood estimators under several common distributions are evaluated. The robust properties of the proposed estimators are discussed with respect to the sample-wise breakdown points proposed by Akritas (1991). Simulation studies are provided in which the performing characteristics of the proposed estimator are compared to that of the nonparametric estimators by Kraemer and Andrews (1982). Interval estimation of the effect sizes is also discussed. In an example, interval estimates for the data set in Kraemer and Andrews (1982) are calculated for both cases A and B.

For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix Γp = Φ1/2Λ′pΨp−1ΛpΦ1/2. This matrix increases with the number of observable variables p. A necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of Γp or, equivalently, divergence of signal-to-noise (Schneeweiss & Mathes, 1995). The same condition is necessary and sufficient for convergence to zero of the positive definite MSE differences of factor predictors, convergence to zero of the distance between factor predictors, and convergence to the unit value of the relative efficiencies of predictors. Various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors.

Optimal sample sizes under a budget constraint for estimating a proportion in a two-stage sampling process have been derived using individual testing. However, when group testing is used, these optimal sample sizes are not appropriate. In this study, optimal sample sizes at the cluster and individual levels are derived for group testing. First, optimal allocations of clusters and individuals are obtained under the assumption of equal cluster sizes. Second, we obtain the relative efficiency (RE) of unequal versus equal cluster sizes when estimating the average population proportion, $$\tilde {>\pi } $$ $$ . By multiplying the sample of clusters obtained assuming equal cluster size by the inverse of the RE, we adjust the sample size required in the context of unequal cluster sizes. We also show the adjustments that need to be made to allocate clusters and individuals correctly in order to estimate the required budget and achieve a certain power or precision.

The biconical trap of Challier and Laveissièr was compared with Langridge's box screen (LBS) and Moloo's awning screen skirt (ASS) for relative efficiency in catching the tsetse species, Glossina pallidipes Austen, in two areas in Kenya. The dark blue biconical trap performed better than the ASS in one area, but both of them caught more males than females. In the other area, the sky blue version of the biconical gave higher yields than LBS and the white biconical. In both areas, the white biconical trap caught the highest proportion of old flies, while ASS caught the highest proportion of young flies. The biconical trap is preferable because it is collapsible, easy to handle and transport, and needs minimal manpower to operate, unlike the LBS and ASS.