2024

Introduction

  • Critical values are values that define the boundaries of the rejection region.

  • The rejection region is the set of values of the test statistic that lead to the rejection of the null hypothesis.

Critical value illustration

The blue area is alpha?

  • Recall that we reject the null if \(P(\bar{x}_{obs} | H_0) < \alpha\).

  • This is equivalent to rejecting the null if \(\bar{x}_{obs} > \text{critical value}\).

  • You can get critical values in R by using functions like qnorm.

Two-tailed critical values

  • These work the same way, but you have to divide \(\alpha\) by 2 and place a critical value on each tail.

Two-tailed critical value illustration