Proposed Nonparametric Tests for the Simple Tree Alternative for Location and Scale Testing in a Mixed Design

Abstract

Six nonparametric tests are proposed for the mixed design consisting of a randomized complete block design (RCBD) and a completely randomized design (CRD). The proposed tests are designed to test for differences in location and/or scale for a simple tree alternative. The tests are a combination of the Fligner-Wolfe test, modified Page’s test, and modified Ansari-Bradley test. A simulation study is conducted to determine how well the proposed tests maintain their significance levels. Powers of the six proposed tests are estimated under a variety of cases: changing the underlying distribution, changing the number of treatments, increasing the variance between the CRD and RCBD portion, changing the proportions of the number of blocks in the RCBD to the sample size for each treatment in the CRD, and changing the parameter arrangements. A recommendation for which test has higher power depends on whether the underlying distribution is symmetric or asymmetric.