Contingency tables are frequently used to present the outcome of a sample of categorical random variables. These variables can also be the result of categorizing the output of continuous random variables. Of interest are, for example, homogeneity or independence between the variables. We focus on two-dimensional tables, where the categories of one variable define the rows and the categories of another variable the columns. Each cell then contains the frequency of occurrence of the row/column combination in the sample. The simplest case is a table:

Here we have two binary random variables and with marginal binomial distribution, or two random variables which are dichotomized into two outcome groups, with labels and . Usually the absolute counts are listed, so is the count of outcome of random variable and outcome of random variable , whereas usually ...

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