STA2201s01 Assignment Three

Quiz on Thursday Febuary 1st. Bring printouts to the quiz. You may be asked to answer questions based on your printouts. You may be asked to hand in one or more of the printouts. The non-computer parts (except maybe question one) are not to be handed in. Do them in preparation for the quiz.

1. A medical researcher is preparing to investigate the effects of two surgical procedures for joint replacement. Essentially there is to be an experimental group receiving a new procedure and a control group receiving the standard procedure. There is a single quantitative dependent variable representing how good the outcome is, and the researcher is entirely comfortable with the usual ANOVA assumptions of normal errors and equal variances. She wishes to detect a difference between µ₁ and µ₂ of 0.4 (in units of the common within-treatments standard deviation sigma), and she wants to do this with probability 0.80.
   1. Derive a simple expression for the non-centrality parameter delta-squared in terms of n1, n2, µ₁, µ₂ and sigma.
   2. Show equal sample sizes are optimal in this case -- by hand.
   3. Find the total sample size needed to attain the researcher's objective. Use S, not the power table in some old book. Bring the printout to class.
2. For a standard two-by-two factorial analysis of variance, what relative sample sizes are optimal (in terms of power) for testing the interaction? Please do this by computer Use my code; bring printout to class.
3. In the second class, we saw that significance tests for the usual linear model (with normal errors) were still of size alpha when the independent variables were random. At the time, I casually stated that the same argument applied to logistic regression. On reflection, I believe this is not so clear at all. What is the problem?