Question

Write out the ANOVA shell (sources of variability & degrees of freedom) for each of the following experiments:

(a) The 4 levels of one treatment variable (Trt) are assigned to EUs in a balanced CRD with 10 replicates per treatment group.

(b) Treatments from a 2-way factorial treatment structure where factor A has 3 levels & factor B has 4 levels are assigned to EUs in a balanced CRD with 6 replicates per treatment.

(c) Five treatments are assigned to EUs in an RCBD with 8 blocks of size 5.

(d) An RCBD with 9 blocks has a 2-way treatment structure where factor A has 3 levels and factor B has 2 levels.

Answer 1

Part a) : Completely Randomised Design.

4 levels of the treatment variable. Let Trt1, Trt2, Trt3, Trt4. 10 replicates per treatment group.

t = 4 and r = 10

Sources of variation	Degrees of freedom
Treatment	t-1 = 3
Error	t*(r-1) = 36
Total	(t*r)- 1 = 39

Part b) : Two-way factorial Experiment with CRD

factor A has 3 levels. a = 3

factor B has 4 levels. b = 4

6 replicates per treatment. r = 6

Sources of Variation	Degrees of freedom
Factor A	a - 1 = 2
Factor B	b - 1 = 3
Interaction AB	(a-1)(b-1) = 6
Error	a*b*(r-1) = 60
Total	(a*b*r) - 1 = 71

Part c) : Randomised Complete Block Design (RCBD)

Number of treatments = t = 5

Number of Blocks = b = 8

Sources of Variation	Degrees of freedom
Blocks	b-1 = 7
Treatments	t-1 = 4
Error	(b-1)(t-1) = 28
Total	(b*t)-1 = 39

Part d) : Two-way Factorial Experiment with RCBD

Number of blocks = r = 9

Levels of Factor A = a = 3

Levels of Factor B = b = 2

Sources of Variation	Degrees of Freedom
Blocks	r - 1 = 8
Factor A	a -1 =2
Error A	(r-1)(a-1) = 16
Factor B	b - 1 = 1
Error B	(r-1)(b-1) = 8
Interaction AB	(a-1)(b-1) = 2
Error	(r-1)(a-1)(b-1) = 16
Total	(r*a*b)-1 = 53

Hope you find the answer helpful.