Statistics for Business: Decision Making and Analysis, 3rd Edition

18.3 General versus Specific Hypotheses

In the previous analytics example, either channel and status are independent or they are not. If the test rejects H₀, the alternative hypothesis does not specify how the proportions differ from independence. Rejecting H₀ implies only that some difference from independence exists, but the test does not specify how the data deviate from H₀. The generality of H_a is good in the sense that the test detects any sort of deviation from independence. For example, managers in this example don’t have to specify how the loan status might differ among the three channels; the test detects any difference among the rates.

This generality comes at a cost. The chi-squared test cannot match the power of a more specific test. ...