Additional methods

There are a number of other measures of association for a variety of circumstances. For example, if one variable is measured on an interval/ratio scale and the second variable is dichotomous (has two outcomes), then the point-biserial correlation coefficient is appropriate. Other combinations of data types (or transformed data types) may require the use of more specialized methods to measure the association in strength and significance.

Other types of association describe the way data are related but are usually not investigated for their own interest. Serial correlation (also known as autocorrelation), for instance, describes how in a series of events occurring over a period of time, events that occur closely spaced in time tend to be more similar than those more widely spaced. The Durbin-Watson test is a procedure to test the significance of such correlations. If the correlations are evident, then it may be concluded that the data violate the assumptions of independence, rendering many modeling procedures invalid. A classical example of this problem occurs when data are collected over time for one particular characteristic. For example, if an epidemiologist wanted to develop a simple linear regression for the number of infections by month, there would undoubtedly be serial correlation: each month’s observation would depend on the prior month’s observation. This serial effect (serial correlation) would violate the assumption of independent observations for simple linear regression and accordingly render the parameter estimates for simple linear regression as not credible.

Inferring causality

Perhaps the greatest danger with all measures of association is the temptation to infer causality. Whenever one variable causes changes in another variable, an association will exist. But whenever an association exists, it does not always follow that causation exists. In epidemiology, the ability to infer causation from an association is often weak because many studies are observational and subject to various alternative explanations for their results. Even when randomization has been applied, as in clinical trials, inference of causation is often limited.