STA 402S98 Assignment 7: Test 2 in tutorial March 13th

The test will cover chapters 19 through 22, skipping the Tukey test for addtivity, and also skipping everything about quantitative independent variables (just use regression), normal probability plots, transformations of the dependent variable, and residual analysis. See Assignments 4, 5 and 6 for more information on what to skip.

In preparation for the test, pay a lot of attention to lecture notes as well as homework and what's in the text. I may ask things I did on the board, directly of indirectly.

Hard copies of the formula sheet should be available on my office door (2092) unless they have all been taken. You can also get a copy here. In preparation for the test,

  1. Using the first expected value line, prove the first equality of the second line.
  2. Again using the first expected value line, prove the first equality of the third line.

You will see SAS output. It will be based on the same data you have used in homework, including the following.

  1. Do problem 21.5 using SAS and a little hand calculation.
  2. Do 22.4 with SAS, assuming that unequal sample sizes do not  reflect unequal importance of treatment means.
  3. Do problem 22.6 a, b, and c. Then set up the SAS command file. The data are in the file CH22PR06.DAT; they are also available here. I hope you agree that in this case the treatment means are of unequal importance. We will assume importance weights proportional to sample sizes, though the sample sizes are too small to provide really good estimates of the relative population sizes.

    First, test for an interaction between subject matter and highest degree, using any appropriate follow-up tests. State your conclusion; not use the word "interaction," and do not use any Greek letters. I would use proc glm for this.

    Next, test whether the population mean earnings per course depends on highest degree. State H0 in terms of µ values (again, assume cell sample sizes are roughly proportional to relative population sizes). Then use proc reg to construct the F-test. Do it with both cell means coding and effect coding. If the results are not identical, you did something wrong. Note that if you want to include ß0 in the null hypothesis when you are doing effect coding, you can use the "variable name" intercept.

    Then, test whether the population mean earnings per course depends on subject matter. State H0 in terms of µ values still assuming cell sample sizes to be roughly proportional to relative population sizes. Then use proc reg to construct the F-test. Do it with both cell means coding and effect coding. Again, if the results are not identical, you did something wrong.