On a rank test in a two-factor mixed model with varying dependent repeated measurements

A rank test for the analysis of a two-factor mixed model with data from n experimental units is studied, where for each factor combination an arbitrary number of repeated dependent measurements is observed, which may grow at a rate of n -super- - ½ - δ,0>δ≤ ½. The proposal covers classical experimental designs, for example the one-way layout and the one factor random block design, and can also be used for meta analyses where data from different designs is combined. Assuming a semiparametric model for the dependent data the asymptotic distribution of the proposed test statistic is derived, and consistent estimators for the asymptotic covariances are proposed. The test statistic is simple to use, automatically adapts to certain commonly used experimental designs, and simplifies in designs with identical replications to simple sums of squares of centered scores. A simulation study suggests that the method can be applied even for moderate sample sizes. Furthermore, the results are applied to a real data set from quality control in clinical chemistry.