STA441 Assignment 9

Quiz in Tutorial on Thursday March 17th

  1. There are 4 first-year calculus courses at UTM. Within each lecture section, a random sample of students was selected and asked about their satisfaction with the course.
    1. What are the factors? Label each one as fixed or random effects.
    2. Of course this a nested design. What factor is nested within what?
    3. Draw a tree diagram of this design.
    4. Write a regression model with cell means coding for this problem. Cell means coding is the scheme with no intercept and a zero-one indicator for each treatment combination. This is too much writing! You are allowed to use "+ ... +" in the middle.
    5. To test for differences between courses, what is the null hypothesis? Answer in terms of the β coefficients from your regression model.
    6. To test for differences between sections within courses, what is the null hypothesis? Answer in terms of the β coefficients from your regression model.

  2. Give your own example of a two-factor experiment in which a fixed-effects factor is crossed with a random-effects factor.

  3. Give your own example of a two-factor experiment in which a fixed-effects factor is crossed with another fixed-effects factor.

  4. Give your own example of a three-factor experiment in which all factors are random effects. B is nested within A, and C is nested within B.

  5. Four plants of the same variety were randomly selected in an experiment to investigate the concentration of a particular acid. Three leaves per plant were randomly selected and three separate determinations of the acid concentration were obtained per leaf. Here are the data in a compact format. For leaf one of plant one, the 3 acid concentrations are 11.2, 11.6 and 12.0. Got it? These data are from Applied linear statistical models (2005, 5th edition) by Kutner et al. 
    Plant           1               2                3                4
Leaf       1    2    3     1    2    3      1    2    3      1    2    3
         --------------  --------------   --------------    --------------
         11.2 16.5 18.3  14.1 19.0 11.9   15.3 19.5 16.5    7.3  8.9 11.3 
         11.6 16.8 18.7  13.8 18.5 12.4   15.9 20.1 17.2    7.8  9.4 10.9
         12.0 16.1 19.0  14.2 18.2 12.0   16.0 19.3 16.9    7.0  9.3 10.5
    1. What are the factors? Are they fixed or random? Nested or crossed?
    2. Make a data file, read the data into SAS, and do a proc print so we can see what you did.
    3. Fit the model with proc glm. Test for variance due to plant and leaf within plant.
    4. Use proc nested to do the same analysis. You should get the same F statistics.
    5. Estimate the proportion of variance in acid concentration that comes from
      • Plant
      • Leaf within Plant
      • Measurement within leaf
      These are numbers from your printout.

  6. In the classical mixed model approach to repeated measures, cases (subjects) is a random effects factor that is nested within combinations of the between-cases factors. In lecture, you saw examples of diagrams that show the nesting/crossing of cases using ovals that cross the within-cases factors.

    Independent random samples of female and male university students viewed ten images of male or female models. The images were either stills or short video clips with a bit of motion but no sound. The response variable in this study was mean rating, so the individual model was not a factor in the experimental design. The idea is that there are three factors: Sex of student, Sex of model, and Still versus motion. For each version of the experiment below, classify each factor as within-cases or between-cases, and make a diagram showing the nesting/crossing of cases.

    1. Each student rated models of only one sex, and saw either all still images or all video.
    2. Each student rated models of both sexes, but saw either all still images or all video.
    3. Each student rated models of both sexes, and saw both still images and video.
    4. Each student rated models of only one sex, but saw both still images and video.


  7. Mantids are insects, kind of like crickets or grasshoppers. When frightened, they emit loud noises that function as alarm calls. I believe they make the sounds by rubbing their hind legs together. The frequency (number of calls per minute) may indicate how alarmed the mantids are. Caged mantids (either Female or Male) were randomly assigned to be exposed to one of four predators (birds), and the number of alarm calls per minute was recorded. Each mantid was tested at three distances from the predator: 8 cm, 13 cm and 18 cm.
    1. What are the cases?
    2. What are the factors?
    3. Classify each factor as within-cases or between-cases.
    4. Make a diagram showing the nesting/crossing of cases.

  8. In a taste test of wine, 6 professional judges judged 4 wines. The numbers they gave do not exactly represent quality. Instead, they are maximum prices in dollars per bottle that the judge thinks the company can charge and still sell most of the wine. I suppose we are assuming that the 6 judges are some kind of random sample, even though they probably are not. The data are available in the file Wine.data.txt. These data are from Applied linear statistical models (2005, 5th edition) by Kutner et al.

    We want to know if there are any average differences among the wines in how expensive the judges think they should be. If so, we want to know which wines are potentially more expensive than which other wines. Carry out the appropriate analysis, with Bonferroni-corrected pairwse comparisons if the initial test is significant. Be ready to state your findings in plain, non-statistical language.

 

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.