9.3 : Critical Region, Critical Values and Significance Level

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.

In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the test statistic (calculated using the sample data) that suggest rejecting the null hypothesis, it is also known as the rejection region or region of rejection. The critical region may fall at the right, left, or both tails of the distribution based on the direction indicated in the alternative hypothesis and the calculated critical value.

A critical value is calculated using the z, t, or chi-square distribution table at a specific significance level. It is a fixed value for the given sample size and the significance level. The critical value creates a demarcation between all those values that suggest rejection of the null hypothesis and all those other values that indicate the opposite. A critical value is based on a pre-decided significance level.

A significance level or level of significance or statistical significance is defined as the probability that the calculated test statistic will fall in the critical region. In other words, it is a statistical measure that indicates that the evidence for rejecting a true null hypothesis is strong enough. The significance level is indicated by α, and it is commonly 0.05 or 0.01.