A contingency table shows the frequencies of two categorical variables as they interact with each other. It is also known as a two-way table, cross tabulation, or cross tab. The frequencies are represented numerically. The totals of each column and each row can be summed in the margins.
Some uses for this table are:
- To examine the relationship between both variables. How do they depend on each other?
- To test a hypothesis.
The chi-square test is used to test a hypothesis, usually starting with the null hypothesis (which is the assumption that there is no difference between the expected and observed result. It uses the percentages of each cell out of the entire sample number in the margins. For more information about contingency tables please check out stat trek or graphpad. For a possibly more in depth explanation of the different parts of a contingency table JMP may be nice. However, note that the information in the latter link must be used in a general sense, as the site is geared towards the explanation of a specific program. Despite that, it is actually quite helpful in distinguishing the different parts of a contingency table.