Glossary

Critical Region

The critical region is the set of values of a test statistic for which the null hypothesis is rejected. It is defined so that, under the null, the probability of the test statistic falling in this region equals the chosen significance level (α).

Definition

Why It Matters

The critical region directly determines the decision rule in hypothesis testing. By specifying which values of the test statistic constitute evidence against the null hypothesis, it establishes the boundary between "reject" and "fail to reject." The size of the critical region is set by the significance level, and its location depends on whether the alternative hypothesis is one-sided or two-sided. Understanding the critical region is fundamental to correctly interpreting test results and avoiding misapplication of statistical tests.

Example

In a two-sided z-test at the 5% significance level, the critical region consists of values below −1.96 or above 1.96. If the computed z-statistic is 2.31, it falls within the critical region, so the null hypothesis is rejected. If the z-statistic is 1.42, it falls outside the critical region and the null is not rejected.

Related Terms

Software Notes

SPSS: Critical values are implicit in test output; examine the p-value and compare to α, or use Transform > Compute Variable to compute critical value boundaries
R: qnorm(0.025) and qnorm(0.975) for two-sided critical values at α = 0.05; qt(0.05, df) for one-sided t-test critical values
Stata: display invnormal(0.025) and display invnormal(0.975) for z critical values; display invttail(df, 0.05) for t critical values