STA442/1008 Assignment 10

Do this in preparation for the Quiz on Friday Dec. 2nd.

  1. Please recall the 2 by 3 factorial design of the Math ACT study described in Assignment 9. In the table below, give the minimum sample size required to obtain a power of 0.90 for each effect, if the effect explains A of the remaining population variation after controlling for other effects in the model. There is no requirement that sample sizes be equal. As usual, we are using alpha = 0.05.

     

      A=0.05 A=0.10 A=0.25
    Main effect for Sex      
    Main effect for Math Background      
    Interaction      
     
  2. For the sample size we do have, what is the power to detect a difference between the marginal means of A and C at alpha = 0.05, assuming that this effect explains 1% of the remaining population variation?
  3. Do a two-way multivariate analysis of variance on the bunny data of Assignment 8. Your dependent variables are force and stiffness. Focus on the main effect for drug. If Wilks' lambda is significant, follow it up with Bonferroni-corrected univariate tests. What do you conclude?
  4. Make up an original experimental study that would employ a three-factor ANOVA with one within-subjects factor and two between-subjects factors. It's important that your example be different from what was presented in lecture and the text. Which one is the within-subjects factor?
  5. Suppose that physicians use a 20-point scale rate the seriousness of the burns for patients in a burn unit, and then the patients rate how much pain they are in at 5 subsequent times.
    1. Viewing this as a multivariate regression, what are the independent variables(s)? What are the dependent variables(s)?
    2. Viewing this as a regression with repeated measures, what are the independent variables(s)? What are the dependent variables(s)? One of the independent variables is within-subjects and one is between subjects. Which is which?
    3. Suppose you are forming linear combinations of the dependent variables to make this a repeated measures analysis. How many linear combinations are you forming? What are they?
    4. Suppose you wanted to test an interaction between the (sort of) quantitative between-subjects independent variable and and the categorical within-subjects independent variable. What would you test? Hint: You would be working with 4 dependent variables. What are they?

Bring your log files and your list files to the quiz.