Nonparametric Tests for the Non-Decreasing and Alternative Hypotheses for the Incomplete Block and Completely Randomized Mixed Design

Abstract

This research study proposes a solution to deal with missing observations which is a common problem in real world datasets. A nonparametric approach is used because of its ease of use relative to the parametric approach that beleaguer the user with firm assumptions. The study assumes data is in an Incomplete Block (IBD) and Completely Randomized (CRD) Mixed Design. The scope of this research was limited to three, four and five treatments. Mersenne - Twister (2014) simulations were used to vary the design and to estimate the test statistic powers. Two test statistics are proposed if the user expects a non – decreasing order of differences in treatment means. They are both applicable in the cited mixed design. The tests combine Alvo and Cabilio (1995) and Jonckheere – Terpstra ((Jonckheere (1954), Terpstra (1952)) in two ways: standardizing the sum of the standardized statistics and standardizing the sum of the unstandardized statistics. Results showed that the former is better. Three tests are proposed for the umbrella alternative. The first, Mungai’s test, is only applicable in an IBD. The other two tests combine Mungai’s and Mack – Wolfe (1981) using the same methods described in the previous paragraph. The same conclusion holds except when the size of the IBD’s sample was equal to or greater than a quarter that of the CRD.