Question

A researcher wanted to examine if soil type had any effects on the heights of daylilies (Y). The thickness of the soil (X) in the pot was used as the covariate X. Given the data that follow, where there are three types of soil (n = 10 in each group),

(a) calculate the adjusted mean values assuming that bw = 0.5, and

(b) determine what effects the adjustment had on the posttest results (describe effects of pre and post adjustment).

Soil Type	Height of daylilies (Y)		Thickness of soil (x)
1	ȳ.₁ = 20		x̅.₁ = 21
2	ȳ .₂ =25		x̅.₂ =18
3	ȳ .₃ =30		x̅.₃ = 15

Answer 1

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AS FOR GIVEN DATA....

The ANCOVA model for this question is given by

1. So if the correlation between Y and X is 0 then there is not effect of soil thickness in the ANCOVA model and hence = 0 implying that the ANCOVA is actually an ANOVA model. Hence MS_with will be same as that of the ANOVA model.

2. If there is substantial negative correlation between X and Y, then the ANCOVA model will explain more variability than the ANOVA one making the error variation less for ANCOVA as comapred to the ANOVA.

3. If the correlation between X and Y changes with the soil type then the is not same for all i = 1,2 3. So the assumption of homogeneity of slopes is violated.

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