Use the Duncan test with the data of Problem 10.16 to determine why the hypothesis of equal means of hardness was rejected.

10-20. A 20-acre field is divided into l-acre plots, with the plots randomly assigned to one of four groups.
For each plot fertilizer is either applied (F) or not applied (NF). For each plot, water is either applied (W) or not applied (NW). Thus, there are five plots for each of the four treatments: (F, W), (F, NW), (NF, W), and (NF, NW). The crop yields in bushels per acre are shown below. Using a 5% level of significance, determine if the within-treatment variances are significantly different. If the null hypothesis of equal variances is accepted, test for a significant difference between group means. If the null hypothesis of equal means is rejected, use the Duncan multiple range to determine if:

(a) the application of water causes a difference: (F, W) and (NF, W) vs. (F, NW) and (NF, NW);

(b) if the application of fertilizer causes a difference: (F, W) and (F, NW) vs. (NF, W) and (NF, NW);

(c) if both fertilizer and water have a significant effect on crop yield: (F, W) vs. (F, NW), (NF, W), and (NF, NW).
(F, W) (NF, W) (F, NW) (NF, NW)
123 117 104 98 118 110 97 95 121 113 112 105 113 99 106 89 126 108 103 100