Hello all,
I am working on a field project where we are evaluating different fertilizer sources applied at 3 different rates! I designed my experiment as a split-plot design with fertilizer being my main plot factor and rate being as my sub-plot factor. I wanted to see if there is an effect of fertilizer source plus rate on plant yield. I created my model but the TukeyHSD letter of differences was weird! The output is showing the second smallest as different from the rest categorized as '1' but the smallest is categorized as '12'. Can anyone help me to decipher it or point out in the right direction?
CISER3<-lme(Yield~Fertilizer+Rate+Fertilizer:Rate, random = ~1|Block/Fertilizer,data = CISER)
anova(CISER3)
numDF denDF F-value p-value
(Intercept) 1 120 126.02571 <.0001
Fertilizer 3 9 1.00131 0.4358
Rate 2 120 2.44039 0.0914
Fertilizer:Rate 6 120 2.66494 0.0184
test4_HSDpost<- cld(emmeans(CISER3,~Fertilizer:Rate,type ="response"),tukey="adjust")
test4_HSDpost
Fertilizer Rate emmean SE df lower.CL upper.CL .group
BM 100 3.750000 0.9434177 3 0.7476239 6.752376 12
WISErg 150 3.850000 0.9434177 3 0.8476239 6.852376 1
Combo 150 4.216667 0.9434177 3 1.2142906 7.219043 12
WISErg 50 4.250000 0.9434177 3 1.2476239 7.252376 12
BM 150 4.383333 0.9434177 3 1.3809573 7.385709 12
Combo 100 4.616667 0.9434177 3 1.6142906 7.619043 12
Combo 50 4.833333 0.9434177 3 1.8309573 7.835709 12
BM 50 4.958333 0.9434177 3 1.9559573 7.960709 12
WISErg 100 5.841667 0.9434177 3 2.8392906 8.844043 2
Tru 150 5.941667 0.9434177 3 2.9392906 8.944043 12
Tru 100 6.216667 0.9434177 3 3.2142906 9.219043 12
Tru 50 6.666667 0.9434177 3 3.6642906 9.669043 12
Degrees-of-freedom method: containment
Confidence level used: 0.95
P value adjustment: tukey method for comparing a family of 12 estimates
significance level used: alpha = 0.05