What should be the degree of freedom in ANOVA table Consider the area under wheat for a sample of 44 clusters
selected from 11 different villages. Four clusters were selected from each of the
11 villages and each cluster consists of 8 survey numbers(fields). Here sum of
squares (SS) due to between villages is 2000, SS due to between clusters within
villages is 8250 and Total SS is 30000. Write the ANOVA table.
My approach
| source of variation  | degrees of freedom  | 
| --------             | --------------      |
| between the villages | 11 -1 = 10          |
| between the clusters | 4-1 = 3             | 
| error                | (11-1)(4-1)         |
| total                | 44-1= 43            |

Now my doubt is that each cluster consists of 8 survey numbers,  then there should be some interaction of clusters and survey numbers
How to incorporate that in degree of freedom ?

So the correct distribution of degrees of freedom is




source of variation
degrees of freedom




between the villages
11 -1 = 10


between the clusters
11(4-1)


error
308


total
44*8 -1




This is the case of two way anova with m observations per cell
