1 Initialize R

Set R to use the sum-to-zero definition of effects and load the police data frame with the following commands:

options(contrasts=c("contr.sum","contr.poly"))
load(url("http://pnb.mcmaster.ca/bennett/psy710/datasets/police20.rda") )

Answer all of the following questions and submit your answers as a script file on Avenue 2 Learn. Make sure to begin your script file with the following lines:

# PSYCH 710 Lab 5 Homework
# Script File
# OCT-2023
# Your Name: <<Your name here>>
# Student ID: <<Your ID here>>
# Collaborators: <<Names of your collaborators here>>

Also, make sure that text that is not an R command is preceded by a comment symbol (#). For example, you can insert questions or comments among your commands like this:

# The following command doesn't work... not sure why...
# ttest(x=g1,y=g2) # was trying to do a t test

2 Police Data

The data frame police contains data from a hypothetical 3x3 between-subjects, factorial experiment. A police department conducted an experiment to evaluate its human relations course for new officers. The independent variables were the type of beat to which officers were assigned during the course (factor beat) and the length of the course (factor course). Each subject was assigned randomly to a single combination of beat and course. The factor beat has three levels: innercity, middleclass, and upperclass. The (unordered) factor course also has three levels: short, medium, and long. The dependent variable is attitude toward minority groups following the course. The data frame also contains a variable, id, which is an id number assigned to each subject.

The following code creates a new factor, condition, that represents the cells in the police experiment, and then plots the data.

# ?interaction # read the help page
police$condition <- interaction(police$course,police$beat)
levels(police$condition) <- c("short.inner","med.inner","long.inner",
                            "short.mid","med.mid","long.mid","short.up","med.up","long.up")
op <- par(no.readonly = T)
par(mar=c(7,4,4,1)+.1)
boxplot(attitude~condition,data=police,xlab="",ylab="attitude",cex.axis=1.2,cex.lab=1.5,las=2)

3 Questions

  1. Use factorial ANOVA to evaluate the main effects beat and course and the beat x course interaction.

  2. Use bartlett.test to evaluate the hypothesis that the variance is equal across conditions/groups.

  3. Inspect the data and suggest a reason why the beat \(\times\) course interaction is significant.

  1. Analyze the main effect of course by performing a linear contrast that evaluates the difference between mean attitude in the short and long course conditions. Also, use an interaction contrast to determine if the result of your comparison of short and long courses depends on the level of beat. Your answer should include the results of the statistical tests (e.g., values of F, t, p, etc.), and your conclusion regarding the null hypotheses for the course contrast and the interaction contrast.
  1. It is possible for us to use a contrast to evaluate the difference between the means in the short and long courses at each level of the beat variable. Suppose you want to evaluate the hypothesis that the value of short-vs.-long contrast in the innercity condition differed from the average of the short-vs.-long contrast values in the middleclass and upperclass conditions. Design a set of contrast weights that you could use to evaluate this hypothesis and then perform the contrast.