Assignment

Note: All answers to be completed in SAS. All SAS input and output must pasted in to the solutions.

Other Statistical software, such as Minitab, JMP, SPSS, R, and MATLAB, are also allowed to use .

1. A clinician is interested in comparing four methods of determining serum amylase in patients with a particular disease. Seven of his patients with the disease volunteered to be in the study. For each patient, a serum specimen was collected and divided into four equal parts. These four parts were then randomly assigned to the four methods. In other words, each patient served as a block. The serum amylase values (enzyme units per ml of serum) are as follows:

1. The clinician would like to consider PATIENT as a random factor. Explain why or why not this is a reasonable consideration.
2. Construct the appropriate ANOVA table and \(F\) -test. Check model assumptions based on your answer to a) and if necessary address any violations.
3. State your conclusions using the \(\alpha=.05\) level.
4. Suppose Treatment 1 is currently considered the gold-standard method. Compare each of the new techniques with the gold-standard, making sure to maintain the FWER at $0.05$.
5. Each of these new methods takes about half the time to run compared to the gold-standard. What new method would you reccomend the clinician further investigate?

2. Suppose that you plan to run a \(p \times p\) Latin square and want to know the power (lower bound) of detecting a difference of size \(D\) between any two of the \(p\) treatments assuming a variance of \(\sigma^{2}\). In a CRD, we use a non-central \(F\) distribution with non-centrality parameter \(\phi=\frac{n D^{2}}{2 \sigma^{2}}\) and degrees of freedom \(a-1\) and \(N-a\) to compute the power. In a standard RCBD, we use the non-centrality parameter \(\phi=\frac{b D^{2}}{2 \sigma^{2}}\) and degrees of freedom \(a-1\) and \((a-1)(b-1)\) to compute the power. What is the form of the non-centrality parameter and degrees of freedom for the Latin Square design?

4. Consider the setup in Montgomery Problem 4-22 but use the data set provided on the course Web page. This is a crossover or repeated measures experiment with BATCH as the experimental unit. Investigate the simple, compound symmetry, and AR(1) correlation structures and report your

results using the best fitting of these correlation structures based on BIC. Don't forget to use method=ML when comparing simple (i.e., standard fixed effects Latin Square analysis) to either of the other two structures.

4.22. The effect of five different ingredients \((A, B, C, D, E)\) on the reaction time of a chemical process is being studied. Each batch of new material is only large enough to permit five runs to be made. Furthermore, each run requires approximately \(1 \frac{1}{2}\) hours, so only five runs can be made in one day. The experimenter decides to run the experiment as a Latin square so that day and batch effects may be systematically controlled. She obtains the data that follow. Analyze the data from this experiment (use \(\alpha=0.05\) ) and draw conclusions.

5. Because Japanese beetles ate the Roma beans in the Oehlerts' garden last year, they ran an experiment this year to determine the best pesticide. They have six garden beds with beans, and the garden store has three different sprays that claim to keep the beetles off the beans. Sprays drift in the wind, so they cannot spray very small areas. Because of this, they divide each garden bed into two plots and use a different spray on the plants in the middle of each plot. After month, they scored the sprayed plant in terms of insect damage using a 0-100 scale, where the higher the score the more damage.

Analyze these data to determine the effects of sprays. Which one should they use?

6. Reanalyze the data from the previous exercise assuming that BED is a random blocking factor with and without DDFM=KR. Write a short summary describing the differences in results. In particular focus on the treatment mean estimates and their differences as well as the standard error of a treatment difference. Which model results would you present and why?

Price: $18.29

Solution: The downloadable solution consists of 9 pages, 929 words and 11 charts.
Deliverable: Word Document