Problem Points Score USE YOUR TIME WISELY USE CLOSEST DF AVAILABLE IN TABLE SHOW YOUR WORK TO RECEIVE PARTIAL CREDIT

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1 Stat 514 EXAM I Stat 514 Name (6 pts) Problem Points Score USE YOUR TIME WISELY USE CLOSEST DF AVAILABLE IN TABLE SHOW YOUR WORK TO RECEIVE PARTIAL CREDIT WRITE LEGIBLY. ANYTHING UNREADABLE WILL NOT BE GRADED Good Luck!!!!

2 1. An instructor wants to evaluate the effectiveness of his teaching assistants. In one class period, the students were randomly divided into equal-sized groups and each group was taught power calculations from one of the assistants. At the beginning of the next class, each student took a quiz on power calculations and these scores (Y ) were compared. The SAS output is shown below. Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total Source DF Type I SS Mean Square F Value Pr > F trt Source DF Type III SS Mean Square F Value Pr > F trt a (3 pts) How many teaching assistants and how many students were involved in this experiment? b (4 pts) Write down the null and alternative hypothesis associated with the F test above. Using α =.05, what is your conclusion?

3 c (3 pts) In addition to the quiz score, the instructor had results on a statistical aptitude test (X) taken at the beginning of the semester. These summaries are presented below. Level of y x trt Mean Std Dev Mean Std Dev Did the random assignment result in reasonably equivalent groups in terms of statistical aptitude? Explain. d (5 pts) The instructor would like to do analysis of covariance. What additional model assumptions must the instructor be aware of when using this method of analysis? Why are they important in terms of inference (i.e., comparing treatments)?

4 e (7 pts) Partial information from the analysis of covariance are shown below. Use these results (and previous information) to assess if there are assistant differences (after adjusting for aptitude). Source Sum of Squares Error Source Type I SS trt x Source Type III SS trt x Standard Parameter Estimate Error t Value Pr > t Intercept B trt B trt B trt B... x <.0001 f (6 pts) Compute the adjusted means using the output above and previous information. How do they compare with those from the original analysis?

5 g (3 pts) In what ways is this second analysis an improvement over the original analysis of variance?

6 2. An experimenter is interested in investigating the effects of two stimulant drugs (A and B) on rats. She equally divided up a total of 20 rats into 5 groups (placebo, Drug A low, Drug A high, Drug B low, and Drug B high) and 20 minutes after injecting the drug recorded each rat s activity level (higher score is more active). Use the results from the following table to answer the following questions. trt mean var 1- Placebo Low A High A Low B High B a (10 pts) Construct the ANOVA table, perform the overall F test and state your conclusion (use α =.05). b (5 pts) State the analysis of variance assumptions and describe one diagnostic (test procedure or plot) that can be used to assess each assumption.

7 c (6 pts) Construct a set of coefficients that will provide the following comparisons: i) Low versus high dosage for Drug A ii) Low versus high dosage for Drug B iii) Drug A versus Drug B iv) Control versus the average of the experimental groups d (3 pts) Which pairs of comparisons are mutually orthogonal? Why? e (6 pts) Complete the following table and, using the Bonferroni correction, state your conclusions. Contrast DF Contrast SS F Value Pr > F a b c 1 d

8 3. For a and b, indicate whether the statement is True or False by circling the appropriate letter. For the remaining parts, provide a clear, concise answer. a. (5 pts) Heidi Seeke performs a randomization test (paired data) and the P-value is T F : If α =.01, she accepts the Null hypothesis T F : If α =.05, she rejects the Null hypothesis T F : If H a is one-sided, the P-value for the two-sided alternative is T F : If α =.01, a Type II error is possible T F : There is a 3.0% chance the Null hypothesis is true T F : If α =.05, a Type II error is possible b. (6 pts) Ivana Noe is designing her experiment involving six different dose levels of a new drug. She is interested in determining the number of mice needed at each dose level. T F : The model degrees of freedom will be 6 T F : More mice will result in a more powerful experiment T F : A larger α will result in a more powerful experiment T F : Using Bonferroni for pairwise comparisons is more powerful than Tukey T F : Using Bonferroni over Tukey will result in fewer Type II errors T F : Using a covariate that only decreases the MS E will decrease the power c. (4 pts) Suppose an investigator is primarily interested in comparing two treatment conditions labeled A and B but adds a third condition C to find out where it falls relative to the other two. He runs the experiment but then seeks your advice because the overall F test comes back insignificant (P >.05) but the comparison of A versus B is significant (P <.05). What do you recommend he do? Explain.

9 d. (4 pts) We briefly discussed in class that analysis of variance is more susceptible to the problems of unequal variance when the sample sizes differ. Assuming the sample sizes are different, would the problem be more or less serious if the small sample groups have the greatest variability? Explain. e. (6 pts) Nondigestible carbohydrates can be used in diet food but they may have effects on colonic hydrogen production in humans. You decide to test and see if insulin, fructooligosaccharide, and lactulose are equivalent in their hydrogen production. You want to construct the test (α =.05) such that it will detect a difference of 15 between any two treatments 95% of the time. If you decide to use n = 6 replicates and preliminary data suggests an error variance of 35, does this meet your goal? Show your work.

10 f. (6 pts) The following ANOVA table is from an experiment where five identically equipped Subaru Outbacks were chosen at random from a dealership and each tested four times for gas mileage. Source Sum of Squares Car 1280 Error 2400 Find estimates of the variance components and the intraclass correlation coefficient.