1. Statistics and Data Analysis Professor William Greene Stern School of Business IOMS Department Department of Economics

2. Statistics and Data Analysis Statistical Tests: Variances

3. Equal Variance Assumption The formula can be used whether the variances of the two groups are the same or not. If it is known that the variances of the two groups are the same, then the results on pages 359-360 in your text can be used to compute a single variance estimator. Why do this? (It’s extra work.) It makes the test procedure more powerful. This will be true whenever you can “pool” data. If the sample size is even moderately large, don’t bother (unless you need to impress someone with your statistical expertise). The change will be trivial and it will not change your conclusion.

4. Equal Variances Computation with Small Samples

5. Unequal Variances In comparing means, the validity (and power) test become dubious if the variances are very unequal. If s A 2 /s B 2 > 2 or < ½, it might be a good idea to reconsider the whole exercise. You can test for unequal variances. Warning: If you do not reject the unequal variances hypothesis, then go on to test equality of the means, you now have two sources of type I error. (Theoretical statisticians worry about this.)

6. A Test for Unequal Variances Assuming both samples are drawn from normal populations with the same variance (the means can be different), the ratio s A 2 /s B 2, has an F distribution. If this F is larger than the upper critical value or lower than the lower critical value, reject the hypothesis.

7. Two Variances Test

8. Equal Variances Test

9. Variance Test: Income vs. Own/Rent 11183.0 2 /17317.6 2 = 0.42