Problems with intrepreting linear mixed model


#1

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


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