# Degrees of freedom due to treatment

let $a$ be the number of treatments.

In Randomized Complete Block Design(RCBD), degrees of freedom due to treatment is $(a-1)$ .

let $k$ be the number of treatments exactly in each block in a Balanced Incomplete Block Design(BIBD).

In BIBD, Adjusted Mean Square due to treatment is given by adjusted sum of square due to treatment divide by degrees of freedom $(a-1)$.

But my question is why do we divide it by $(a-1)$? .Since it is adjusted , why don’t we divide it by $(k-1)$?

• In mean square error of treatment we pooled the effect of treatments thats why it is $a-1$. and $k-1$ is the degree of freedom of block, here we are interested in block effect. – SAAN Aug 9 '13 at 13:49
• @Azeem But The degree of freedom is not $k-1$. It is $b-1$ so written on the book.$b$ = number of blocks & $k$ is defined above. – ABC Aug 9 '13 at 18:34
• In your stated example $b & k$ are equal, thats why I say that. – SAAN Aug 10 '13 at 1:53
• @Azeem I apologize. I forgot to mention $k<b$ – ABC Aug 10 '13 at 3:52
• Keep in mind general rule of degree of freedom that is $n-k-1$ where $n$ denotes number whose effect is to be tested, $k$ is number of parameters estimated (here is zero). – SAAN Aug 10 '13 at 6:41