In this assignment, you will employ the multivariate approach to repeated measures.
- For the Furnace data, carry out a two-factor analysis of variance in which the dependent variable is energy consumption, and the independent variables are type of vent damper, and whether the vent damper is active or inactive. What is the situation here?
- Both variables between cases
- Both variables within cases
- One between and one within
For each main effect and the interaction, be able to give the F statistic and p-value. Be able to interpret any significant test using simple, non-statistical terms.
- For the Salmon data, carry out a three-factor analysis of variance in which the dependent variable is growth, and the independent variables are country, gender, and fresh vs. marine. Designate each independent variable as between or within. For each main effect and each interaction, be able to give the F statistic and p-value.
The following should help you interpret your findings. All the significant tests involve just two of the three independent variables. Using a spreadsheet program such as Excel, graph the significant two-way interaction. Make sure your graph is nicely labelled; several examples have been given in class. Print your graph; you will hand it in. If you do not already know how to proudce graphs using Excel, you will need to figure it out. This should not be impossible, since milions of people can do it.
- From the graph, it is clear that one of the significant main effects should be interpreted, and the other should not. For the main effect that should be interpreted, state the conclusion in simple, non-statistical language.
- The other significant main effect should not be interpreted. Why not?
- Interpret the interaction in simple, non-statistical language.
- In a study of the psychology of attention, subjects attempted to solve
word problems while listening to distracting backgound noise. The distracting material was either music, or spoken words related to the problem they were trying to solve. The distracting material was presented at three different levels of loudness. Each subject attempted 10 problems at each combination of loudness and type of distraction, for a total of 60 problems. Order of presentation was randomized. Data for each subject are number correct in each of the six treatment combinations, and are avalable in
distract.data
Carry out the appropriate two-factor analysis, obtaining F-tests for both main effects and the interaction. Follow up the analysis with all pairwise differences among treatment means, using ordinary matched t-tests with a Bonferroni correction (You could use custom contrasts, but this is easier and the answers are the same). Your follow-up tests suggest that the interaction and one of the main effects (not the other one) should be interpreted. State your conclusions in plain language. Also, prepare a graph of the means using Excel of a similar program. You will hand this in.