A Maximum Test for the Analysis of Ordered Categorical Data

Abstract

Different scoring schemes are possible when performing exact tests using scores on ordered categorical data. The standard scheme is based on integer scores, but non-integer scores were proposed to increase power (Ivanova & Berger, 2001). However, different non-integer scores exist and the question arises as to which of the non-integer schemes should be chosen. To solve this problem, a maximum test is proposed. To be precise, the maximum of the competing statistics is used as the new test statistic, rather than arbitrarily choosing one single test statistic.

A general score‐independent test for order‐restricted inference

“…We propose a generalization of the MAX test 14 that can be applied to more general order-restricted inference problems. The new test is embedded into a flexible framework for conditional inference procedures.…”

“…It is well known that the maximum of a sequence of optimal test statistics leads to an efficiency robust test procedure and that the efficiency robustness properties depend on the correlation between the optimal statistics under the null hypothesis. 34 To test the global null hypothesis of independence between X and Y, taking the extensive search over the collection of order-restricted sets into account, we use (6). It is also possible to test the partial null hypotheses of independence associated with each set of order-restricted scores.…”

“…In practice, ordinal variables are often assigned a set of order‐restricted scores in an attempt to represent the true relative distances between the categories. The problematic issue of assigning a set of scores to ordinal variables has been discussed exhaustively by several authors . The choice of scores is typically subjective, and different scores may even lead to conflicting conclusions.…”

“…The problematic issue of assigning a set of scores to ordinal variables has been discussed exhaustively by several authors. [2][3][4][5][6][7][8] The choice of scores is typically subjective, and different scores may even lead to conflicting conclusions. Therefore, several score-independence test procedures have been proposed.…”

“…Therefore, several score-independence test procedures have been proposed. [9][10][11][12][13][14] However, all these approaches are limited to the case of ordered 2 × K tables, where K is the number of ordered categories.…”