Class Notes – Monday 23 January 2006

 

Last Class

·      distributions include parameters we wish to estimate (CI’s) or test (HT’s);

·      usual Wald CI paradigm (estimate +/- 2 SE) works well in simple cases, but breaks down sometimes;

·      could then use the Wald paradigm on another scale and then “back-transform” – e.g., odds ratio (p.3);

·      when the above fails, use likelihood or other methods;

·      SLR where X is a “dummy variable” for one of the treatments is equivalent to the equal-variance two independent sample t-test;

·      this helps us extend to ANOVA and ANOCOV;

·      homework due Weds. 1st Feb; $35.00 cash or check due this week for Course Notes.

 

New Material

·      SLR assumptions – impt. to consider/meet;

·      Interpretation of slope parameter estimate is very impt. (bottom of p.2);

·      Ex. 2 illustrates transforming both sides of the equation (not done so much anymore), and complication with interpretation of slope in this case;

·      Parameter estimates (b0 and b1) are random variables and are usually correlated – confidence ellipses;

·      MLR: several potential X’s can be included, individual t-tests are one-at-a-time tests given other X’s in the model;

·      If we want to simultaneously drop several X’s (and in other cases as well), we must use the Full-and-Reduced F test on p.8 – this test is very important!

·      The above test is a special case of the -2DLL test – this latter test stat. finds the change in the LogLikelihood and doubles this, and it has a c2 distribution;

·      Dummy variables revisited in 2.5, and then applied to ANOCOV, for which we first test for parallelism (make sure interaction term is insignificant), and then look for a difference between the two groups after adjusting for the covariate(s) – this finishes 2.6.