Ch 15 - 43E

Chapter 15, Problem 43E

(choose chapter or problem)

Consider the Friedman statistic  when  and  number of blocks . Then, \(F_{y}=(2 / n)\left(R_{1}^{3}+R_{2}^{3}\right)-9 n\). Let  be the number of blocks (pairs) in which treatment one has rank 1. If there are no ties, then treatment 1 has rank 2 in the remaining  pairs. Thus, \(R_{1}=M+2(n-M)=2 n-M\) Analogously,\(R_{2}=n+M\). Substitute these values into the preceding expression for  and show that the resulting value is \(4(M-5 n)^{2} / n\) Compare this result with the square of the  statistic in Section 15.3. This procedure demonstrates that \(F_{y}=Z^{2}\).

Equation transcription:

Text transcription:

F{r}=(2 / n)\left(R{1}^{3}+R{2}^{3}\right)-9 n

R{1}=M+2(n-M)=2 n-M

R{2}=n+M

4(M-5 n)^{2} / n

F{r}=Z^{2}