The Oedered Alternatives Test Problem Based On Aligned Ranks In Complete Block Design

In complete block design,we must to solve the ordered alternatives test problem in order to compare the treatment effects.At present,we most often used the Page test to solve that problem. In the Page test,the ranks from samples are drawn by sorting the observations in each block. In this paper,we give a test named W test based on Aligned Ranks for the first time to solve the ordered alternatives test problem,the aligned ranks from aligned observations are drawn by sorting the aligned observations after wiping off the treatment effects. It is different to the ranks such as in the Page test.This paper have 7 parts. In part l,we introduced the two hypothesis test problem in complete block design,and introduced the most methods to solve the two problem, then analysed the Rank, Aligned Rank and Ties. In part 2, we gave the W test statistic by computing the product-moment correlation coefficient on the paired-wise data. In part 3,we discussed the W test in complete block design with each experiment unit have only one observation, because there will exist ties in aligned observations,we gave the Expectation and Variance of the W statistic in these conditions under the null hypothesis. In part 4 and 5,we discussed the W test in complete block design with each experiment unit have repeat observations, because there will exist ties in aligned observations,we gave the Expectation and Variance of the W statistic in these conditions under the null hypothesis. In part 6, we proofed that the asymptotic distribution of the W statistic is normal distribution under large sample assumption,in practise, we could make decision by asymptotic pvalue. In part 7, we gave the particular process to solve the ordered alternatives test problem by applying the W test, and analysed a example.