Abstract
In this article, a new test based on Jonckheere test [1] for randomized blocks which have dependent observations within block is presented. A weighted sum for each block statistic rather than the unweighted sum proposed by Jonckheereis included. For Jonckheere type statistics, the main assumption is independency of observations within block. In the case of repeated measures design, the assumption of independence is violated. The weighted Jonckheere type statistic for the situation of dependence for different variance-covariance structure and the situation based on ordered alternative hypothesis structure of each block on the design is used. Also, the proposed statistic is compared to the existing test based on Jonckheere in terms of type I error rates by performing Monte Carlo simulation. For the strong correlations, circular bootstrap version of the proposed Jonckheere test provides lower rates of type I error.
Highlights
In medical research, testing the direction change or trend of response levels over time/treatment is very considerable problem
The group of repeated measures can be analyzed by parametric methods to uncover the mean profile change with ordered alternatives
The modification of Jonckheere tests were developed in order to make use of information contained blocks that have dependent observations
Summary
In medical research, testing the direction change or trend of response levels over time/treatment is very considerable problem. Zhang and Cabilio [3] developed a generalized Jonckheere test against ordered alternatives for repeated measures in a randomized block design. Crossover or changeover designs, time series designs and before-after designs are used in this kind of situations Both Jonckheere and Page tests are based on rank correlations between the within-block rankings and the criterion alternative ranking. Cabilio and Zhang [3] used a generalized version of Jonckheere statistic based on MK statistics for testing the ordered alternative hypothesis They obtained the asympyotic distribution of this statistic and used different dependent structure for this testing procedure. As seen from their simulation study, the obtained empirical type I error rates are not close to their nominal levels sufficiently.
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