Question 9.11: Three fertilizers are studied for their effect on yield in a...
Three fertilizers are studied for their effect on yield in an orange grove. Nine plots of land are used, divided into blocks of three plots each. A randomized complete block design is used, with each fertilizer applied once in each block. The results, in pounds of harvested fruit, are presented in the following table, followed by MINITAB output for the two-way ANOVA. Can we conclude that the mean yields differ among fer1ilizers? What assumption is made about interactions between fertilizer and plot? How is the sum of squares for error computed?
\begin{array}{cccc}\hline \text{Fertilizer}& \text{Plot 1}& \text{Plot 2}& \text{Plot 3}\\\hline \text{A}& 430 & 542 & 287 \\\text{B}& 367 & 463 & 253 \\\text{C}& 320 & 421 & 207 \\\hline\end{array}
Two -way ANOVA: Yield versus Block. Fertilizer
\begin{array}{lrrrrr}\text{Source}& \text{DF}& \text{SS}& \text{MS}& F & P \\\text{Fertilizer}& 2 & 16213.6 & 8106.778 & 49.75 & 0.001 \\\text{Block}& 2 & 77046.9 & 38523.44 & 236.4 & 0.000 \\\text{Error}& 4 & 651.778 & 162.9444 & & \\\text{Total}& 8 & 93912.2 & & &\end{array}Our explanations are based on the best information we have, but they may not always be right or fit every situation.
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