STA442/1008 Assignment 9

Do this in preparation for the final exam

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. Thre 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. 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, do males and females perfome differently on average? 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. Does the magnitude of the sex difference in performance depend on upon profile of course work in High School math? Answer Yes or no.
  8. If (and only if) the answer is Yes, graph the interaction and perform the appropriate Bonferroni-corrected follow-up tests. If you have a conclusion, state it in plain language.
  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?

Bring your log file and your list file to the exam. You may need to hand one or both of them in.