Unit 5 Hypothesis Testing: Two Samples

Every test so far compared a sample against a number that came from outside the data — a government figure, a manufacturer’s specification, a dean’s estimate.

Most questions worth asking are not shaped like that. They compare two groups.

Do men and women earn different wages for the same work? Do students from government schools perform differently from those from private schools? Does the high-yielding variety of wheat out-yield the conventional one? Did the villages that received the road see incomes rise more than those that did not?

In each case there is no external claim to test against. There are two groups, each with its own sample mean, and the question is whether the difference between them is larger than sampling variation alone would produce.

This unit builds that test. It also brings us to a distinction that will occupy the rest of the book: the difference between establishing that two groups differ, and establishing that something caused them to differ.