Testing for Independence

Suppose we want to know if people who smoke are more likely to get cancer than people who don't smoke.

Such a question requires testing for independence. In this case we are trying to see if the chance of getting cancer is related to smoking.

The test statistic is based on the chi-square distribution and is the same as with tests for homogeneity.

The null hypothesis assumes independence, while the alternative assumes dependence.
Or in other words, the null says that smoking doesn't cause cancer, while the alternative states that smoking does cause cancer.

Often, plotting the data in a table can give a convincing overview, i.e.:

		Smoke
		Yes	No
Cancer	Yes	68	16
	No	9	7

Please note that the data in that table is fictional, and only used for example purposes. Also, please know that presentation of a data in a table, while effective, is not a substitute for statistical testing.