a.)Based on this ANOVA table, how many replicate plants did we use for each pest

Question

a.)Based on this ANOVA table, how many replicate plants did we use for each pesticide/fertilizer treatment combination?

b.)What conclusions can we draw from this ANOVA table about the effects of the pesticide on plant biomass?

c.)From this ANOVA table, can we tell if the effects of the various fertilizers on plant biomass are beneficial or harmful?

d.)Is there a significant interaction between the effects of the pesticides and fertilizers on plant biomass?

e.)What is the statistical model that we are fitting to our biomass data in this analysis?

Extra credit question: What fraction of the variation in biomass can be explained by this model?

we are interested in the effects of several different pesticide treatments, fertilizers, and any potential interactions between pesticides and fertilizers, on the biomass of an annual plant We set up a 2-way fully factorial design, crossing all combinations of pesticides fertilizers The experiment has a balanced design (meaning that the same number of replicate plants was used for every pesticide/fertilizer treatment combination), and we recorded the biomass of each plant at the end of the growing season. We conducted an analysis of variance in R (with biomass weight as the response variable) and obtained the following partial ANOVA table 1. Analysis of Variance Table Response: weight Source p-value (or, is the p- value

Explanation / Answer

a)

number of pesticides a-1=2 a=3

number of fertilizers =b-1=3 b=4

number of . replicates ab(r-1) =36

r = 4

b)

calculating the MS =SS/DF

F = MSi/MSe

i = fert, pest, pest:fert

we see that for pesticide F > Fcritial

so the results are sginiifcant

c)

from f table F pest > F critical

so results are significant

d)

as F > Fcritial

there are siginificant interaction effects.

df SS MS F Fcritical Fert 2 142.288 71.144 19.32458596 3.2317 pest 3 44.174 14.72466667 3.999607651 2.8387 fert:pest 6 62.702 10.45033333 2.838586034 2.3359 residual 36 132.535 3.681527778

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