Analyze A 2x2 Contingency Table - GraphPad

Assumptions of 2x2 contingency tables

Contingency tables and the tests listed above require the assumptions below to be met:

• Independence among the sample
• Unpaired subjects
• Analyzing counts (not percentages)
• Correct tabular set up

For more details, see our analysis checklist.

Example experiment setup

Suppose you recruit a fixed number of people with and without lung cancer. Then you interview each subject and record whether they are smokers or not. Notice these are both factors with exactly two possibilities.

This study would correspond to a contingency table like the one below, where you could count the number of subjects in each of the four categories. Testing the differences between the observed and expected counts can help you quantify the relationship between smoking and lung cancer.

Lung Cancer Healthy Smoking Non-smoking

Chi-square test calculation details

Chi-square tests compare the observed (O) and expected (E) frequencies of the subjects. With contingency table tests, the expected frequencies are calculated in the background based on the multiplication rule of probability. The idea is to use the row and column (marginal) totals to calculate the expected counts if there is no association between the variables. If the observed values vary significantly from the expected values (using a chi-square test), then there is statistical evidence of association.

The formula is: