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Page, Jonckheere, Hollander tests are the most common non-parametric tests for ordered alternative pattern in randomized blocks where contain independent observations. However, when randomized blocks include correlated observations, properties of null distribution for these tests under independence cannot be applied to the situations where randomized blocks contain dependent observations. Circular bootstrap versions of these tests are suggested to test for ordered alternative hypothesis in randomized blocks which include correlated measurements when the underlying distributions are not known. In this study the effect of correlation coefficient, number of treatment/time point and block sizes on type 1 error and power values of some existing non-parametric test statistics based on the circular bootstrap method are taken into consideration with a stationary auto regressive process. The significance levels and power values of these tests based on circular bootstrap method are simulated by using the statistical software package R, 3.4.2. Based on findings in the simulation study, circular bootstrap version of original Page Test provides better power values among other trend statistics. Finally, these circular bootstrap-based non-parametric tests are applied to a real life dataset.

Comparison of non-parametric tests of ordered alternatives for repeated measures in randomized blocks