Decision Rule

In the context of statistical hypothesis testing, decision rule refers to the rule that specifies how to choose between two (or more) competing hypotheses about the observed data. A decision rule specifies the statistical parameter of interest, the test statistic to calculate, and how to use the test statistic to choose among the various hypotheses about the data. More broadly, in the context of statistical decision theory, a decision rule can be thought of as a procedure for making rational choices given uncertain information.

The choice of a decision rule depends, among other things, on the nature of the data, what one needs to decide about the data, and at what level of significance. For instance, decision rules used for normally distributed (or Gaussian) data are generally not appropriate for non-Gaussian data. Similarly, decision rules used for determining the 95% confidence interval of the sample mean will be different from the rules appropriate for binary decisions, such as determining whether the sample mean is greater than a prespecified mean value at [Page 337]a given significance level. As a practical matter, even for a given decision about a given data set, there is no unique, universally acceptable decision rule but rather many possible principled rules.

There are two main statistical approaches to picking the most appropriate decision rule for a given decision. The classical, or frequentist, approach is the one encountered in most textbooks on statistics and the one used by most researchers in their data analyses. This approach is generally quite adequate for most types of data analysis. The Bayesian approach is still widely considered esoteric, but one that an advanced researcher should become familiar with, as this approach is becoming increasingly common in advanced data analysis and complex decision making.