A contingency table is a way of summarising the relationship between variables, each of which can take only a small number of values. It is a table of frequencies classified according to the values of the variables in question.
Higher classifications are also possible.
It may be enhanced by including the percentages that fall into each category. Sometimes we are interested in the proportion of responses that fall into one of two categories. A confidence interval for a proportion would specify a range of values within which the true population proportion may lie, for such examples. The procedure for obtaining such an interval is based on the proportion, p of a sample from the overall population. Many occasions arise where we have to compare the proportions of two different populations.