TABLE 12-19
an Agronomist Wants to Compare the Crop

TABLE 12-19
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows.
$$\begin{array} { l l l l } \text { Fields } & \text { Smith } & \text { Walsh } & \text { Trevor } \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$$ Below is the Minitab output of the Friedman rank test:

Friedman Test: Yield versus Varieties, Fields

Friedman test for Yield by Varieties blocked by Fields
$\mathrm { s } =$$10.00$ $\quad \mathrm { DF } = 2 \quad \mathrm { P } = 0.007$

$\begin{array}{lllc} & & \text { Est } & \text { Sum of } \\\text { Varieties } & \mathrm{N} & \text { Median } \\\text { Smith } & 5 & 13.500 & 5.0 \\\text { Trevor } & 5 & 15.667 & 10.0 \\\text { Walsh } & 5 & 18.533 & 15.0 \\\\\text { Grand median }= &15.900\end{array}$

-Referring to Table 12-19, the Friedman rank test is valid only if there is no interaction between the 5 blocks and the 3 treatment levels.