# Truth about the population H0 TrueH1 True

 Correct decision Type II error Type I error Correct decision

(b) Example

Courtroom Verdict Not Guilty

Guilty

Defendant Not Guilty Guilty

 Correct decision Wrongfully acquitted Wrongfully accused Correct decision

selected frequently. The value of 0.05 is equivalent to a 95% 'confidence limit' while a of 0.01 represents a 99% confidence limit. When we select the significance level (a) of a test, we are setting the probability of a type I error ('wrongfully accused'). Small p-values lead to rejection of the null hypothesis (and acceptance of the alternative hypothesis) while large p-values favor the null hypothesis.

The null hypothesis is rejected when the computed p-value lies in the region of rejection, which is usually p < 0.05. Rejection of the null hypothesis implies acceptance of the alternative hypothesis. When multiple analyses are being performed simultaneously for significance testing, the Bonferroni correction may be applied (D.N.A. Box 19.2).

It is important to recognize that by chance 5% of tests will have p-values below p = 0.05. Thus, just because a test of significance is below a certain value, the null hypothesis should not necessarily be rejected. 