STA442/1008 Assignment 11

Quiz in Tutorial on Friday Nov 27th

  1. Suppose you have a data set with a quaqntitative dependent variable Y, quantitative independent variables X1 and X2, and factors A, B and C. Factor A has 3 levels (categories), factor B has 2 levels and factor C has 3 levels. You see this SAS code; 
                    proc glm;
                class A B C;
                model Y = X1 X2 A|B|C;
    1. Is this an analysis of covariance? Answer Yes or No. If Yes, what are the covariates?
    2. Indicate how you would define dummy variables for the factors, using effect coding. Use names like a1, a2, and so on.
    3. Write E(Y|X=x) for a regression model equivalent to the proc glm model above.
    4. For the initial F-test produced by proc glm,
      1. State the null hypothesis in terms of β quantities from your regression model.
      2. How many (numerator) degrees of freedom will be in your test?
    5. For each of the following effects in the proc glm model, state the null hypothesis in terms of β quantities from your regression model.
      1. Main effect of A.
      2. Main effect of B.
      3. Main effect of C.
      4. A by B interaction.
      5. A by C interaction.
      6. B by C interaction.
      7. A by B by C interaction.
    6. Controlling for the covariates, are there any differences among the 18 treatment means? State the null hypothesis you would test in order to answer this question. You answer should be in terms of β quantities from your regression model.

  2. Please revisit the infamous bunny data. Do a two-way multivariate analysis of variance, with time and drug as the independent variables, and force and stiffness as the dependent variables. The tests of interest are those for the main effect of time, the main effect of drug, and the drug by time interaction. Of these, the main effect for drug is by far the most important.

    Following up any significant multivariate tests with the corresponding univariate tests using a Bonferroni correction, what do you conclude? Remember, the primary purpose of the study is to find out whether the drug increases bonding of the false tooth to bone. Note that this assignment is asking for a lot less detail than Assignment 10 did, so you can just cut out a lot of material when you edit (a copy of) your SAS program.

  3. In a study of the psychology of attention, subjects attempted to solve word problems while listening to distracting backgound noise. The distracting material was either music, or spoken words related to the problem they were trying to solve. The distracting material was presented at three different levels of loudness. Each subject attempted 10 problems at each combination of loudness and type of distraction, for a total of 60 problems. Order of presentation was randomized. Data for each subject are number correct in each of the six treatment combinations, and are avalable in distract.data

    Carry out the appropriate two-factor analysis, obtaining F-tests for diffeences among the 6 treatment means (this is the overall test), and also for both main effects and the interaction. Follow up the analysis with all pairwise differences among treatment means, using ordinary matched t-tests with a Bonferroni correction (You could use custom contrasts, but this is easier and the answers are the same). Your follow-up tests suggest that the interaction and one of the main effects (not the other one) should be interpreted. State your conclusions in plain language. Also, prepare a graph of the means using Excel or a similar program. You will hand in the graph as part of the quiz.

    If you don't own Microsoft Office, good for you! You are innocent and pure. You can download Open Office for free at http://www.openoffice.org

 

Please bring your log file and your list file to the quiz. As usual, answers to the questions are not to be handed in. They are just practice for the quiz. Please do not write anything on your printouts except your name and student number.