Question

Yield of wheat can be affected by Fusarium, a fungus. Antifungal agents can be researched by measuring their impact on wheat yield in bushels per acre. A trial of five different antifungal agents could be conducted on four blocks of land, with each divided into five plots, and one randomly assigned for each agent. Do a complete hypothesis test to compare the effectiveness of antifungal agents.

Antifungal A B C D E
1 41.1 37.7 34.2 32.2 39.9
2 40.2 35.4 38.2 32.7   40.1
3 39.9 41.1 39.4 38.9 41.2
4 37.2 40.5 37.7 36.8 42.1

Answer 1

Using two-way ANOVA we can test to compare the effectiveness of antifungal agents.

Here the hypothesis is,

H0: Mean effects are equal vs H1: Mean effects are not equal

Here the ANOVA table is,

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Antifungal agents	75.925	4	18.98125	4.725328	0.016016	3.259167
Blocks	30.7495	3	10.24983	2.551667	0.104558	3.490295
Error	48.203	12	4.016917
Total	154.8775	19

Here the p-value for the above hypothesis is 0.016016 < 0.05 but >0.01. So, at 1% level of significance, we don't have enough evidence to conclude that the effects are significant but at 5% level of significance, we can conclude that there is a significant difference in the effects of antifungal agents.