Nonparametric Tests for the Umbrella Alternative in a Mixed Design for Location
This paper further investigates existing test statistics proposed by Magel et al. (2010) for detecting umbrella alternatives when the peak is known, and the underlying design consists of a completely randomized design (CRD) and randomized complete block design (RCBD). Magel et al. (2010) assumed equal variance between the CRD and the RCBD portions for the power estimates that they conducted. We investigate the powers of the tests compared to each other when testing for location in this design when the variance of the CRD portion is 2, 4, and 9 times larger than the variance of the RCBD portion. Underlying normal, t, and exponential distributions are considered as well as a variety of location shifts, and different ratios between the sample size in the CRD portion compared to the number of blocks in the RCBD portion.
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