Stat 514 Exam II Fall 2011

Name: ______

1. Given the following layout:

Block
1 / 2
Treatment / 1 / XX / X
2 / X / XX

a) Write out the model including the Main Effects and the error term (no interaction).

b) Given the model in a), if I were to use the average of the responses for Treatment at level one, minus the average of the responses for Treatment at level two, what does this estimate in terms of the model parameters?

c) Is the estimate given in part b) an unbiased estimate of the difference of Treatment means? Why?

d) From lecture, would the design of part a) be considered an orthogonal design? Why?

2. In a materials experiment, I have six samples of from the same source of aggregate. I randomize my samples to one of two asphalt cement concentrations, 4.5% or 5.5% (three to each). After mixing with the asphalt cement, each sample is subdivided into three subsamples and baked at 300 degrees C for 40, 60 or 80 minutes (in the same oven, they are all put in and then subsamples are taken out at 40, 60 or 80 minutes). Afterward, each subsample is measured for “Creep”, which is an indicator of softness.

a) Draw the layout.

b) Write out the model.

c) Write out the ANOVA table with Source, df and EMS using the algorithm.

d) Which are the more sensitive F-tests in the ANOVA? Why?

3. In a study designed to study the efficacy of alternative treatments for ADHD, thirty children diagnosed with ADHD were recruited for the study. They were randomly assigned to one of three groups (ten to a group). Group I received a Placebo, Group II received a standard dose of Ritalin (methylphenidate), Group III received neurofeedback training. The experiment was conducted over a two month period. Each subject was tested for ADHD symptoms using the Conner’s scale prior to the experiment and post experiment.

a) Draw the layout.

b) Write out the model.

c) Write out the ANOVA table with Source, df and EMS using the algorithm.

d) If I did not include Subject in the model, which F-statistics would likely be larger or smaller? Why?

4. Suppose you were given all of the data from the experiment described in question 3.

a) Prior to the experiment, I randomized the subjects to Treatment groups in order to eliminate any systematic bias in my results. Analyzing only the data collected prior to the experiment using the Connor’s scale, how could you check to be sure that the randomization did what it was supposed to do? What should the result of your analysis show?

b) One would expect that the Placebo group would have no difference in the Connor’s scores prior to vs. post experiment. What is the easiest Statistical test you would run to show this?