A Method Expanding 2 by 2 Contingency Table by Obtaining Tendencies of Boolean Operators: Boolean Monte Carlo Method

A medical test and accuracy of diagnosis are often discussed with contingency tables. However, it is difficult to apply a contingency table to multivariate cases because the number of possible categories increases exponentially. We hypothesize that randomly assigning Boolean operators and focusing on frequencies of Boolean operators could explain the outcome correctly, obtain the tendencies of operators, and overcome difficulties in analyzing large numbers of variables and categories. The aims of this paper are introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases. To test this method, we construct two types of data: 1) when variables and outcome were randomly determined and 2) when the outcome depends on one variable. Analysis of the first type of data by this method showed that there was no significant result. Analysis of the second type of data reflected the bias of the data. As far as we know, this is the first attempt to use a frequentist approach to randomly assigned Boolean operators.