Critical Value

Critical values are used in hypothesis testing to delimitate two regions: one in which the analyst rejects the null hypothesis and another in which the hypothesis cannot be rejected. Therefore, critical values are closely linked to the concept of hypothesis testing. For instance, in a two-sided t test to compare two sample means, if the sample sizes are 21 and 21, so that we have 40 df, the critical value for a 0.05 level of significance (i.e., a 95% level of confidence) is 2.01 (this value can be found in tables for the Student's t test). If the computed t statistic is, say, 2.32, we reject the null hypothesis—that the two samples correspond to two populations with the same population mean—at the 0.05 level of ...