Question: A completely randomized design was used to study the effects of five different soil amendments on growth of a particular plant species. Each treatment group, including a no amendment “control” group was replicated three times for a total N = 18 observations. The treatments were defined as follows:

A: compost + Nitrogen

B: compost + Nitrogen + Potassium

C: peat moss + Phosphorus

D: peat moss + Nitrogen + Calcium

E: peat moss + Calcium + Potassium

F: no amendments (the control)

You wish to make the following comparisons using contrasts:

i) the effect of Nitrogen vs. no Nitrogen

ii) the effect of compost vs. peat moss

iii) the effect of fertilizer “blends” vs. single nutrient additions

a. Derive numeric contrast coefficients for each treatment group to estimate the contrast values.

b. Which of the above contrasts are orthogonal to each other?

c. If the MSE for this study turned out to be 11, compute the standard error for contrast i)

Nitrogen vs. no Nitrogen.