Chapter 1: Hypothesis Testings With Three or More Population Groups

While the methods described earlier can be used to compare two population means, it is sometimes necessary to compare three or more population means. Such comparisons will be examined here.

t-Tests can be used to compare three or more groups. In order to test the hypothesis that “the three population means are equal to each other (H₀: µ₁ = µ₂ = µ₃)”, three “t-Test of the Difference between Two Population Means” should be applied for the analysis of the hypotheses given below:

This approach is not efficient. Each test is based on the probability that the null hypothesis is true. Therefore, every test is subject to the risk of a Type I error. A Type I error is the rejection of a true hypothesis. The probability level (α) set as the point of rejection of the null hypothesis is the risk encountered. With this probability of 0.05, the rejection of the null hypothesis is incorrect in 5 out of 100 t-Test runs. In other words, if α = 0.05, it means that we accept the risk that the rejection of the null hypothesis will be incorrect 5 times out of 100. This problem is known as the multiple comparison problem. It occurs when a large number of hypothesis tests are performed. In this case, we are confident that five of the tests will reject the null hypothesis, which is true, leading to a wrong decision.