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 Maximum Test for the Analysis of Ordered Categorical Data,"
Journal of Modern Applied Statistical Methods: Vol. 8
, Article 24.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss2/24