STA442/1008 Assignment 9

Do this in preparation for the Quiz on Friday Nov. 25th

The file mathACT.dat. contains data based on a 1987 administration of the ACT Mathematics Assesment test, a standardized multiple choice test sometimes given to screen American High School students for admission to university. There are three variables: Sex, Course work in High School mathematics, and score on the test. Students were selected so that they met one of three common profiles of Course work in High School mathematics, labelled a, b and c in the data file. They are:

  1. Algebra I only
  2. Two algebra courses and geometry
  3. Two algebra courses, geometry, Trigonometry, Advanced Mathematics and Beginning Calculus

Now please answer the following questions.

  1. What are the independent variables? What is the dependent variable?
  2. Is this study experimental, observational, or both? Why?
  3. Make dummy variables for the independent variables using effect coding -- that's the scheme with the minus ones for the last category. Using proc reg, test for both the main effects and the interaction with no Bonferroni correction. You would be silly not to check your work with proc glm. For each effect, state the proportion of remaining variation explained.
  4. Averaging across different High School math backgrounds, is there a significant difference between the performance of males and females? If so, who does better on average?
  5. Averaging across sex, is course work in High School mathematics related to achievement on the Math ACT?
  6. If the answer to the preceding question is Yes, follow up with Bonferroni-corrected pairwise comparisons of marginal means. I believe it will be easier to do this in a separate proc reg run with a different dummy variable coding scheme. Or, you can do the algebra if you really want to. State your conclusions in non-statistical language.
  7. Controlling for other effects in the model, what proportion if the remaining sample variation in the dependent variable is explained by the main effect of High School course work in mathematics? The answer is 0.4095304.
  8. Does the magnitude of the sex difference in performance depend on upon profile of course work in High School math? Answer Yes or No Conclusion.
  9. Based on this study, a High School counsellor advises entering students that if they want to do well on the ACT, they should take a lot of math courses. The advice may be good, but the evidence is flawed. Why?
  10. Pretend that the data have not been collected yet. In Table the table below, please give the minimum sample size required for significance at the 0.05 level for each effect, if the effect explains a of the remaining sample variation after controlling for other effects in the model. There is no requirement that sample sizes be equal.

     

      a=0.05 a=0.10 a=0.25
    Main effect for Sex      
    Main effect for Math Background      
    Interaction      
    For the sample size we did have, what proportion of the remaining sample variation needed to be explained in order for the interaction to be significant? Is that pathetic, or what?

Bring your log files and your list files to the quiz. You may need to hand them in. I have two log files and two list files.