Write out the ANOVA shell (sources of variability & degrees of freedom) for each of the following experiments described below. Identify all factors in the ANOVA that should be treated as random in the analysis.
A split-plot experiment has a 2X3 factorial whole-plot treatment structure where treatment factor A has 2 levels and treatment factor B has 3 levels. Each combination of A & B was randomly assigned to 5 different whole plots in a CRD for a total of 30 whole plots. Each whole plot was divided into 4 subplots and the 4 levels of treatment factor C were each randomly assigned to one subplot within each whole plot.
| Source | d.f. |
| (Whole plots) | |
| Block | r - 1 |
| Factor A | a - 1 |
| Whole plot error |
(r - 1)(a - 1) |
| (Sub plots) | |
| Factor B | b - 1 |
| A × B | (a - 1)(b - 1) |
| Sub plot error | a(r - 1)(b - 1) |
| (Sub-sub-plots) | |
| Factor C | c - 1 |
| A × C | (a - 1)(c - 1) |
| B × C | (b - 1)(c - 1) |
| A × B × C | (a - 1)(b - 1)(c - 1) |
| Sub-sub plot error | ab(r - 1)(c - 1) |
| Total | (rabc) - 1 |
The ANOVA shell is:
| Source | d.f. |
| (Whole plots) | |
| Block | 5- 1 |
| Factor A | 2 - 1 |
| Whole plot error |
(5 - 1)(2 - 1) |
| (Sub plots) | |
| Factor B | 3 - 1 |
| A × B | (2 - 1)(3 - 1) |
| Sub plot error | 2(5 - 1)(3 - 1) |
| (Sub-sub-plots) | |
| Factor C | 4 - 1 |
| A × C | (2 - 1)(4 - 1) |
| B × C | (3 - 1)(4 - 1) |
| A × B × C | (2 - 1)(3 - 1)(4 - 1) |
| Sub-sub plot error | 2*3(5 - 1)(4 - 1) |
| Total | (5*2*3*4) - 1 |
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