1 Initialization

Initialize R with the following commands:

options(digits=4,width=80)
options(contrasts=c("contr.sum","contr.poly") )  # set definition of contrasts
load(url("http://pnb.mcmaster.ca/bennett/psy710/datasets/tetrahymena.rda") )
load(url("http://pnb.mcmaster.ca/bennett/psy710/datasets/leprosy.rda") )

2 Tetrahymena Data

Much of the material in this section was based on Section 10.7 in Introductory Statistics with R by Peter Dalgaard.

An experiment was conducted to examine the factors that influence growth in Tetrahymena cells. What is/are Tetrahymena? From Wikipedia:

Tetrahymena is a genus of free-living ciliates that can also switch from commensalistic to pathogenic modes of survival. They are common in freshwater ponds. Tetrahymena species used as model organisms in biomedical research are T. thermophila and T. pyriformis.

Figure 1: Tetrahymena thermophila. (Taken from Wikipedia)

Figure 1: Tetrahymena thermophila. (Taken from Wikipedia)

The experiment grew Tetrahumena cells in two groups of cultures that either did or did not include glucose. The primary research question whether glucose affected the diameter of cells. At the start of the study, the investigators measured the cell concentration (count per ml) for each cell culture. The data are stored in the data frame tetrahumena, which contains the two-level factor glucose and the numeric variables diameter, conc (cell concentration), and logConc ( log(cell concentration) ).

  1. Conduct an analysis of variance to evaluate the effect of glucose on diameter.

  2. Conduct an analysis of covariance to evaluate the effect of glucose on diameter after controlling for the effect cell concentration. Conduct two ANCOVAs: one that uses conc as the covariate, and another that uses logConc as the covariate.

  3. Regarding the previous question: Which ANCOVA is better? Why?

  1. Do the results of the ANCOVA (that uses logConc as the covariate) depend on the order of terms in the model? Why or why not?
  1. If the order of the terms does affect the coefficients of the ANCOVA model, which order do you think is better? Why?
  1. Calculate Cohen’s \(f\) and partial Cohen’s \(f\) for the effect of glucose after controlling for the effect of the covariate. Why do the two values differ?
  1. Evaluate the homogeneity of slopes assumption.

3 Leprosy Data

An experiment examined the effect of drugs on the treatment of leprosy. A measure of the abundance of leprosy bacilli on the skin was calculated for each participant. Participants were then randomly assigned to one of three treatment conditions (\(n=10\) per group) that involved taking an antibiotic or a placebo daily for several months. At the end of the experiment, a measure of the abundance of leprosy bacilli was taken again on each participant. The data are stored in the data frame leprosy which contains the numeric variables baseline and postTreatment and the three-level factor drug. The levels in drug represent two antibiotics (A and B) and a control group (placebo).

  1. Use the analysis of variance to evaluate the effect of drug on postTreatment. Use Tukey pairwise tests to compare the three groups.

  2. Use the analysis of covariance to evaluate the effect of drug on postTreatment after controlling for baseline. Check the homogeneity of slopes assumption. Then use Tukey HSD tests to evaluate pairwise differences among the adjusted means.

  1. Explain why the effect of drug was significant in the ANOVA but not the ANCOVA.