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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) $?

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  • $\begingroup$ 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. $\endgroup$ – SAAN Aug 9 '13 at 13:49
  • $\begingroup$ @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. $\endgroup$ – ABC Aug 9 '13 at 18:34
  • $\begingroup$ In your stated example $b & k$ are equal, thats why I say that. $\endgroup$ – SAAN Aug 10 '13 at 1:53
  • $\begingroup$ @Azeem I apologize. I forgot to mention $k<b$ $\endgroup$ – ABC Aug 10 '13 at 3:52
  • $\begingroup$ 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). $\endgroup$ – SAAN Aug 10 '13 at 6:41

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