STA441 Assignment 10

Quiz in Tutorial on Thursday March 24th

  1. 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 the file distract.data.txt. Don't forget to look at the data before you start analyzing it.
    1. How many factors are there in this study? Classify each one as between cases or within cases.
    2. Make a picture showing the nesting/crossing of cases.
    3. Using the classical mixed model approach to repeated measures, carry out the appropriate analysis, obtaining F-tests for all main effects and interaction(s). You could follow up the analysis with Bonferroni corrected matched t-tests, but don't bother this time.
    4. By requesting a straight two-factor between-cases ANOVA from proc glm, you can get an interaction plot without much effort. Please do it.
    5. Your plot suggests that the interaction and one of the main effects (not the other one) should be interpreted. Which main effect should not be interpreted, and why?
    6. Because the sample size is so large, you can assume that everything you see is significant, so don't bother with follow-up tests this time. State your conclusions in plain language.
  2. The CO2 uptake of six plants from Quebec and six plants from Mississippi was measured at several levels of ambient CO2 concentration. Half the plants of each type were chilled overnight before the experiment was conducted. The data are available in the file CO2.data.txt.
    1. How many factors are there in this study? Classify each one as between cases or within cases.
    2. Make a picture showing the nesting/crossing of cases.
    3. Use proc tabulate to make a table of sample means. Look at them.
    4. Using the classical mixed model approach to repeated measures, carry out the appropriate analysis, obtaining F-tests for all main effects and interaction(s).
    5. It is really helpful to look at the mean plots. You can get what you need from proc glm; please do it. Remember, proc glm gives you a plot when there are 2 factors. I wound up with two such plots, one for Quebec plants and one for Mississipi plants. CO2 concentration was on the x axis. I played around with the order of variables on the class statement to get this.
    6. With the classical mixed model approach to repeated measures, multiple comparisons can be a serious challenge. We won't do it this time. Instead, just look at your two beautiful plots, and describe the 3-factor interaction in plain, non-statistical language.
  3. This question takes you back to logistic regression. In a logistic regression with dummy variables, an interaction (represented as usual by products of dummy variables) means that one or more odds ratios for factor A depend on the level of factor B. So as usual, an interaction means "it depends." For the Berkeley graduate admission data (see Assignment 7), is the Sex by Department interaction statistically significant at the 0.05 level? If so, you can assume it's because something different is going on for Department A; see Chapter 4 in the text. You don't have to do any follow-up tests.

 

Please bring BOTH your log files and BOTH your your results files to the quiz. As usual, answers to the questions are not to be handed in. They are just practice for the quiz. Please do not write anything on your printouts except your name and student number. It is okay to highlight the results file, but do not write interpretations on your results files, or cause them to appear in any way (including comment statements) on your log files.