Contingency tables

Contingency tables summarize results where you compared two or more groups and the outcome is a categorical variable (such as disease vs. no disease, pass vs. fail, artery open vs. artery obstructed).

Contingency tables display data from these five kinds of studies:

•In a cross-sectional study, you recruit a single group of subjects and then classify them by two criteria (row and column). As an example, let's consider how to conduct a cross-sectional study of the link between electromagnetic fields (EMF) and leukemia. To perform a cross-sectional study of the EMF-leukemia link, you would need to study a large sample of people selected from the general population. You would assess whether or not each subject has been exposed to high levels of EMF. This defines the two rows in the study. You then check the subjects to see whether or not they have leukemia. This defines the two columns. It would not be a cross-sectional study if you selected subjects based on EMF exposure or on the presence of leukemia.

•A prospective study starts with the potential risk factor and looks forward to see what happens to each group of subjects. To perform a prospective study of the EMF-leukemia link, you would select one group of subjects with low exposure to EMF and another group with high exposure. These two groups define the two rows in the table. Then you would follow all subjects over time and tabulate the numbers that get leukemia. Subjects that get leukemia are tabulated in one column; the rest are tabulated in the other column.

•A retrospective case-control study starts with the condition being studied and looks backwards at potential causes. To perform a retrospective study of the EMF-leukemia link, you would recruit one group of subjects with leukemia and a control group that does not have leukemia but is otherwise similar. These groups define the two columns. Then you would assess EMF exposure in all subjects. Enter the number with low exposure in one row, and the number with high exposure in the other row. This design is also called a case-control study.

•In an experiment, you manipulate variables. Start with a single group of subjects. Half get one treatment, half the other (or none). This defines the two rows in the study. The outcomes are tabulated in the columns. For example, you could perform a study of the EMF/leukemia link with animals. Half are exposed to EMF, while half are not. These are the two rows. After a suitable period of time, assess whether each animal has leukemia. Enter the number with leukemia in one column, and the number without leukemia in the other column. Contingency tables can also tabulate the results of some basic science experiments. The rows represent alternative treatments, and the columns tabulate alternative outcomes.

•Contingency tables also assess the accuracy of a diagnostic test. Select two samples of subjects. One sample has the disease or condition you are testing for, the other does not. Enter each group in a different row. Tabulate positive test results in one column and negative test results in the other.

For data from prospective and experimental studies, the top row usually represents exposure to a risk factor or treatment, and the bottom row is for controls. The left column usually tabulates the number of individuals with disease; the right column is for those without the disease. In case-control retrospective studies, the left column is for cases; the right column is for controls. The top row tabulates the number of individuals exposed to the risk factor; the bottom row is for those not exposed.

Logistic regression

Contingency tables analyze data where the outcome is categorical, and where there is one independent (grouping) variable that is also categorical. If your experimental design is more complicated, you need to use logistic regression which is available in Prism. Logistic regression is used when the outcome is categorical, specifically when the outcome is binary (yes/no, alive/dead, pass/fail, etc.). In some cases, you may only have one independent variable (X variable) as a predictor for this outcome. In this case, you can use simple logistic regression. Additionally, if there are multiple independent variables, which can be categorical or numerical, you can use multiple logistic regression. To continue the example above, imagine you want to compare the incidence of leukemia in people who were, or were not, exposed to EMF, but want to account for gender, age, and family history of leukemia. You can't use a contingency table for this kind of analysis, but you can use logistic regression.