Observations on two responses are collected for three treatments. The observatio

Question

Observations on two responses are collected for three treatments. The observation vectors [x_1 x_2] are Treatment 1: [6 7], [5 9], [8 6], [4 9], [7 9] Treatment 2: [3 3], [1 6], [2 3] Treatment 3: [2 3], [5 1], [3 1], [2 3]. (a) Break up the observations into mean, treatment, and residual components as we did in class. Construct the corresponding arrays for each variable. (b) Using the information in Part a), construct the one-way MANOVA table. (c) Evaluate Wilks's Lambda A" and use the table presented in class to test for treatment effects.

Explanation / Answer

The data is arranged in a spreadseet first as follows:

The data is imported into the R statistical software and the MANOVA is fitted to obtain the Wilk's lambda:

> tt <- read.csv("clipboard",sep=" ")
> class(tt$Treatment) <- 'factor'
> tt$Treatment
[1] T1 T1 T1 T1 T1 T2 T2 T2 T3 T3 T3 T3
Levels: T1 T2 T3
> tr.manova <- manova(cbind(tt[,2],tt[,3])~tt$Treatment)
> summary(tr.manova,test="Wilks")
             Df   Wilks approx F num Df den Df    Pr(>F)   
tt$Treatment 2 0.03619   17.027      4     16 1.283e-05 ***
Residuals     9                                            
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Treatment x1 x2 T1 6 7 T1 5 9 T1 8 6 T1 4 9 T1 7 9 T2 3 3 T2 1 6 T2 2 3 T3 2 3 T3 5 1 T3 3 1 T3 2 3

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