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 b_w = 0.5, and (b) determine what effects the adjustment had on the posttest results.

$\begin{array}{l}\begin{array}{ccc}\text { Soil Type}&\text { Heights of Daylilies (Y) }&\text { Thickness of Soil }\\\hline 1 & \bar{Y}_{1}=20 & \bar{X}_{.1}=21 \\2 & \bar{Y}_{.2}=25 & \bar{X}_{22}=18 \\3 & \bar{Y}_{3}=30 & \bar{X}_{3}=15 \\\hline\end{array}\end{array}$

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 b_w = 0.5, and (b) determine what effects the adjustment had on the posttest results.

\begin{array}{l}\begin{array}{ccc}\text { Soil Type}&\text { Heights of Daylilies (Y) }&\text { Thickness of Soil }\\\hline 1 & \bar{Y}_{1}=20 & \bar{X}_{.1}=21 \\2 & \bar{Y}_{.2}=25 & \bar{X}_{22}=18 \\3 & \bar{Y}_{3}=30 & \bar{X}_{3}=15 \\\hline\end{array}\end{array}

Quizplus · Accepted Answer

The Answer is (a) Adjusted mean: . We know that = 20, = 25, = 30; b_w = 0.5; = 21, = 18, = 15. Because it's a balanced design, = (21 + 18 + 15)/3 = 18. We can calculate
20 ? 0.5*(21 - 18) = 18.5;
25 ? 0.5*(18 -18) = 25;
30 ? 0.5*(15- 18) = 31.5.

(b) The adjustment moved the mean for Group 1 down by 1.5 units (from 20 to 18.5), and moved the mean for Group 3 up by 1.5 units (from 30 to 31.5). It did not change the mean for Group 2. Therefore, after the adjustment the difference between group means is enlarged. The effects of soil type will become larger and possibly more significant.

A Researcher Wanted to Examine If Soil Type Had Any