TABLE 12-19
an Agronomist Wants to Compare the Crop Yield

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$

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

-Referring to Table 12-19, the decision made at a 0.01 level of significance on the Friedman rank test for the difference in medians implies that all 3 medians are significantly different.