STA442/1008 Assignment 6

Quiz in tutorial on Friday March 7th

1. For the TV data, compare the mean assessed value of home for the Urban, Rural and Small-town locations. If the initial test is significant, follow up with Scheffé-protected pairwise comparisons, and also comparisons of each location to the average of the other two. That's six follow-up tests, out of the infinitely many that are possible. For each test,
   1. What is the estimated value of each contrast you are testing? Use estimate or bring a calculator to the quiz.
   2. What is the value of the test statistic? The answer is a number. This means you must set up the pairwise comparisons yourself.
   3. What critical value are you using?
   4. What is your conclusion, if any? (Be able to state it in plain language.)

   The remainder of the assignment is based on Chapter Four, Handout 6, and associated lecture material.
    

2. In a study of customer satisfaction, a random sample of customers were surveyed for three retail outlets of a drug store chain, with two floor managers for each outlet. Thus, two independent random samples of customers were surveyed for each store, one for each manager.
   1. In the table below, make columns (how many?) giving contrasts for testing differences among outlets. Leave some room for the next part.
       

      Outlet	Manager
      1	1
      1	2
      2	1
      2	2
      3	1
      3	2

   2. Now create columns with the contrasts for Manager nested within Outlet.
   3. Suppose the drug store chain has many outlets, and at least three or four floor managers for each outlet; they are on duty at different times. Describe how the data would be collected if both outlets and managers within outlets were random effects. How would it be different if they were fixed effects?
   
    
3. Give original examples of two-factor studies (crossed, not nested), with
   1. Fixed effects
   2. Random effects on both factors.
   3. One fixed factor and one random (a mixed model).
   It does not matter whether these are three separate studies, or just different ways of doing the same study.
    
4. In an experiment to study the effect of oven temperature upon the crustiness of bread, three temperatures were compared (1 = Low, 2 = Medium, 3 = High). Six huge "batches" of dough were prepared in the usual way, and these are regarded as a random sample from the population of all batches (fairly reasonable, and very typical). Two batches were randomly assigned to be cooked at each temperature, three loaves of bread were randomly selected from each batch for testing, and the "Crustiness" of each loaf was judged by expert tasters.

   In this experiment, the case is the loaf of bread. It is an example of "subsampling," which logically yields a nested design.

   The data are available in the file bread.data.

   The main question is whether crustiness of bread depends on temperature. A secondary question is whether there is any difference in crustiness from batch to batch. Carry out the appropriate tests. For each one, be able to state the numerical value of the test statistic and the p-value, and be able to describe the results in plain language. If the effect of temperature is significant, follow it up with Scheffé tests. (What are the denominator degrees of freedom?) Why would you not follow up the on Batch effect even if it is significant?