Modified Extended Median Test for C Matched Samples

Abstract

Abstract:This work presented an extended median test for analyzing samples that are not independent but paired or matched given some criteria. Here, the data for analysis are presented in table form with the column corresponding to one factor with 'c' treatments or conditions considered as fixed, while the row as second factor with say 'k' subjects ,batches, blocks or levels which are considered random given that there is only one observation per cell. These observations themselves may be measurements on as low as the ordinal scale. The null hypothesis to be tested was that there is no difference between the 'c' treatments, thus having equal medians. This required the use of Friedman test and an alternative ties adjusted method. Although these methods lead to the same conclusions, the relative sizes of the calculated chi-square values suggest that the Friedman test is likely to lead to an acceptance of a false null hypothesis (Type II error) more frequently and hence likely to be less powerful than the ties adjusted modified extended median test. Nevertheless, the Friedman's two-way analysis of variance test by ranks is here at least shown to be still more powerful than the usual extended median test.