Assignment 8
Hand this assignment in during class on Tuesday April 6th if you want to be done. If you want more time, put it in my mailbox before midnight on Tuesday April 13th.
The file salmon.dat contains growth data for a sample of Alaskan and Canadian salmon. Apparently, growth during different time periods can be estimated by the diameter of rings in a fish's scales. We have two measurements of growth during our fishes' first year of life -- marine growth (in the ocean) and freshwater growth.
The variables are:
| country: | 1=Alaskan 2=Canadian |
| sex: | 1=Female 2=Male |
| fresh: | Diameter of rings for first-year freshwater growth in 100ths of an inch |
| marine: | Diameter of rings for first-year marine growth in 100ths of an inch |
Please conduct two sets of analyses, using the union-intersection approach to multiple comparisons. We're in the world of the normal linear model, so these are Scheffé tests. The first set of analyses will be univariate, and the second set will be multivariate.
Compute a new variable, equal to the sum of growth in freshwater and marine environments. This will be your dependent variable.
The null hypothesis of the initial test is that all four "treatment" means are equal. If it is rejected, explore the data using Scheffé followups. I'd like you to use the following strategy.
Do a healthy number of tests, certainly including tests for both main effects and the interaction. Don't discuss the ones that fail to reject H0. Once you have reached your conclusions, write them on the printout in the margin beside the test or tests that justifies it. Be informative; talk about fish. For example, you would not say "The null hypothesis µ11+µ21 = µ12+µ22 is rejected." You would say "Male fish have greater average growth than female fish." Or something like that.
Turn in the complete program file (fish.sas or whatever, and also the list file (fish.lst, with your hand-written conclusion or conclusions.
For this part you can use my SAS code from the handout if you want. It will save you some typing, especially for the critical value of lambda.
Considering marine growth and freshwater growth simultaneously as two dependent variables, please do the same kind of thing you did for the univariate case. Start with a handwritten sheet in which you give the L, ß and M matrices for your initial H0: LßM=0. Is your initial univariate test above a proper followup to the one you specify here? Answer Yes or No.
Now calculate the critical value of Wilks' lambda; I get a critical value of 0.9365173. Then do the follow-up tests. Your follow-ups should include at least one univariate test and at least one multivariate test. Again, please turn in the program file, and the list file with your conclusions written on it.
If you saw an earlier version of this assignment, you'll notice that I cut out all that stuff about editing your list file.