A Non-Parametric Maximum for Reasonable Number of Rejected Hypotheses: Objective Optima for False Discovery Rate and Significance Threshold in Exploratory Research with Application to Ordinal Survey Analysis

This paper identifies a criterion for choosing the largest set of rejected hypotheses in high-dimensional data analysis where Multiple Hypothesis testing is used in exploratory research to identify significant associations among many variables. The method neither requires predetermined thresholds for level of significance, nor uses presumed thresholds for false discovery rate. The upper limit for number of rejected hypotheses is determined by finding maximum difference between expected true hypotheses and false hypotheses among all possible sets of rejected hypotheses. Methods of choosing a reasonable number of rejected hypotheses and application to non-parametric analysis of ordinal survey data are presented.