## What is a Rejection Region?

Aliases: *critical region*

A rejection region (a.k.a. critical region) in a Null Hypothesis Statistical Test is a part of the parameter space such that observing a result that falls under it will lead to the rejection of a the null hypothesis. In hypothesis testing usually a significance test is performed and the rejection region is given in the form of a statistic such as a t score or a z score. It can just as easily be given in terms of the actual (non-standardized) parameter value.

A rejection region has a one-to-one correspondence with the significance threshold as it is simply a more technical way to express it. Since a standardized score is expressed in terms of standard deviations (e.g. 1.644 SD or .1.96 SD) it is directly specifying the area under the parameter distribution which will lead to rejection which can easily be turned into alpha (α) during the planning stage or a p-value after the test is completed by computing the cumulative distribution function.

After the test is completed, the observed p-value is compared to the critical Z score which is at the boundary of the rejection region and if it falls with the region the null hypothesis is rejected.

Notably, if a value is not within the rejection region this does not automatically mean that the null hypothesis can be accepted: it merely states that there is not enough evidence to warrant rejecting it.