Bivariate data without an explanatory variable

In some bivariate categorical data sets, one variable can be treated as a response whose value depends on the other explanatory variable. The explanatory variable can then be used to split the individuals into groups.

In other bivariate data, the relationship between the variables is more symmetrical but we still want to discover whether particular values of one variable are associated with values of the other. A contingency table again summarises the data.

    Variable X
Variable Y       X1       X2       X3   
  Y1 105 7 11
Y2 58 5 13
Y3 84 37 42
Y4 57 16 17