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Homework #9

This homework is based on the “mireault.txt” data set, described in Howell, page 689–690. We will be interested in the three-way ANOVA with “perceived vulnerability to loss” as the dependent variable and group, gender, and year in college as the independent variables. Because this is not a true experiment, subjects could not be randomly assigned and thus we have an unbalanced design.

Also, be careful when you import this data file. There are missing data (sometimes subjects won’t report things when asked to), and sometimes software packages interpret that to mean the variables are “string” variables rather than “numeric” variables. If this happens to you, you can fix it by editing the type of variable so that it is read as being numeric.

Problem 1

Present two tables (with marginals), one for each gender, of the ns in each cell. There should be a total of 3 x 2 x 4 = 24 cells (12 in each table). What’s the ratio of the largest n to the smallest n?

Problem 2

Run the three-way ANOVA. (Don’t worry about heteroscedasticity or outliers for this one.) Report the relevant inferential statistics.

Problem 3

You can never have too much practice at interpreting interactions. There is a two-way interaction in this data set. What is it?

First, plot the marginal means, either weighted or unweighted (your choice, but be clear which you did in the caption), that are relevant for interpreting that interaction. This should be a publication quality plot.

Now, describe what the interaction looks like. Next, interpret that interaction with something more precise than your eyeballs. Training wheels off here, you have to figure out what to do and what it means. You are free to use any technique that we’ve discussed (simple main effects, interaction contrasts, posthocs on cells), but justify your choice, and be sure to provide tests that support your interpretation.

Problem 4

There is at least one reliable main effect here. Which one(s)? Produce publication-quality plot(s) for the reliable main effect(s), describe them, and then attempt to say something more specific than “somebody is different than the grand mean.” You will be graded on how clear and specific your interpretation is. (Yes, one of these main effects is involved in the interaction, so normally you wouldn’t bother with it, but go ahead and interpret it anyway. You need the practice.)

Note

The other new thing you’re getting in this homework is that these are real data, and real data are often messy. There are missing values here for many subjects for various measurements. If any subject is missing a measurement on the DV, you can’t use them. If any subject is missing a measurement on any IV that you’re using, you can’t use them.

Notes for R

R shouldn’t have any difficulties importing the data type when you read in the file, but it will do odd things with factors when there are missing values for IVs. When you explicitly designate factors in R, make sure the factor is defined only on the levels that actually exist. To do this, note that the “factor()” function in R takes a “levels” argument, so you can restrict the factor to only certain levels that appear in the data file, such as restricting it to only 1 through 3, but leaving out any 4s or undefined levels.