Unit 13: Chi-square Tests

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 Teaching Tips

• Students need to learn how and when to use the chi-square tests. Just as before, there is value in understanding why the formula has its structure, but little value in simply memorizing the formula.

• However, students should be able to compute the expected counts in a goodness of fit test. (In other words, they should be able to perform some of the intermediate steps required to compute the statistic.) It's a very good learning excercise for students to do the same (compute expected counts) in the two-way table (for tests for independence or homogeneity).

• The TI83/TI84 doesn't do goodness-of-fit tests automatically. But it can be coerced into doing so if you enter the data via two lists.

• The "chi-square statistic" will only have (approximately) a chi-square distribution if the number of expected counts in all cells is at least 1, and no more than 20% of the expected counts are less than 5. That's a good rule-of-thumb to follow, similar to the np>10 and n*(1-p)>10 that we check before using the normal approximation to the distribution of p-hat. There are other rules of thumb published as well, and any of them will do.

Student Misconceptions and Confusions

• The null hypothesis in the test for independence is that the variables ARE independent. Rejecting the null means that you are deciding that they are NOT independent and therefore related. This strikes some students as a little backwards, because independence is made to seem so rare and interesting. But remind them that usually you want to prove that two variables are related (dependent), not unrelated (independent). So the null (rhymes with "dull") position would be that they are not related.

Resources

• It's tricky to teach students why the chi-square statistic in the context of a test of independence is a measure of lack of independence. If you want some more information on this as well as how to determine the degrees of freedom for chi-square tests, visit the NCSSM site and click on "Chi-square Analyses by Dan Teague, 2003".

• The General Social Survey (http://www.norc.org/GSS+Website/) has a seemingly endless list of variables that can be used for in-class examples or assignments.