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Analysis of Messy Data Volume 1: Designed Experiments

George A. Milliken, Dallas E. Johnson

Chapter 10

Using the Effects Model to Analyze Balanced Two-Way Treatment Structures with Unequal Subclass Numbers - all with Video Answers

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Chapter Questions

01:14

Problem 1

Consider the experiment described in Exercise 9.1
1) Analyze the data with SAS-GLM using an effects model. Include the following options on the MODEL statement: E, El, E3, and SOLUTION. Also have GLM calculate the estimates of the drug main effect means, the disease main effect means, and the two-way means and have GLM do pairwise comparisons between these three sets of means.
2) Write out the hypotheses being tested by the type I analysis using the notation of the means model as was done in Table 10.8, where $\mu_{i j}$ represents the expected response to drug $i$ and disease $j$. Express these in terms of the effects model.
3) Write out the hypotheses being tested by the type III analysis in terms of the means model.
4) Write out the hypotheses being tested by the type II analysis in terms of the means model.
5) Restate the following hypotheses in terms of the effects model and use CONTRAST and/or ESTIMATE statements with the effects model to determine the observed significance levels for the following hypotheses:
a) $\left(\bar{\mu}_{1 \cdot}+\bar{\mu}_2\right) / 2=\bar{\mu}_{3 *}=\bar{\mu}_4$.
b) $\mu_{11}=\mu_{12}=\mu_{13}$.
c) $\left(\bar{\mu}_{1 \cdot}+\bar{\mu}_{2 \cdot}\right) / 2=\bar{\mu}_{3 *}$.
d) $\mu_{12}=\mu_{22}=\mu_{32}=\mu_{42}$.
e) $\bar{\mu}_{3 *}-\bar{\mu}_{\mathrm{i}+}=0$.
f) $\mu_{12}-\mu_{13}-\mu_{32}+\mu_{33}=0$.
g) $\mu_{22}-\mu_{32}=0$.

Manik Pulyani
Manik Pulyani
Numerade Educator

Problem 2

Using the data from Exercise 8.1 where the sample sizes in each cell are equal, demonstrate that the type I, type II, type III, and type IV analyses are identical.

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01:18

Problem 3

Verify that the Drug LSMEANS for 10.1 are the averages of the two-way cell means.

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:31

Problem 4

Use the method described in Section 10.4 to compute the type III analysis for the data set in Example 6.1. Use GLM to verify your results.

Jameson Kuper
Jameson Kuper
Numerade Educator