I am working on a field project where I am evaluating different fertilizer sources (4) applied at 3 different rates(50, 100 and 150)! I designed my experiment as a split-plot design with fertilizer source being my main plot factor and rate being as my sub-plot factor. I wanted to see if there is an effect of treatment (fertilizer source), rate and treatmentrate on plant yield. I created my model but I am not sure if it right. Plus I wanted to see if there is any difference between the blocks (total 4) with fertilizer source and rate.
I ran the anova codes first and it indicated that the interaction term treatmentrate is highly significant. However, when I ran the TukeyHSD the letter of differences were off!
The letter of differences in the Tukey HSD is weird. I am getting the same standard error for all my treatments plus the lowest yield was observed in BM 100 (donated as 12 in TUKEY HSD). It should be one as it has the lowest mean. Furthermore, if you look down at the table treatment Tru 50 has the highest yield but it is donated with 12 numbering whereas, WISErg 100 is donated with number 2 but it is certainly not the highest mean.
The letters/numbers of difference and standard errors just don't make sense to me and I am not quite sure what wrong with it. Can anyone explain it to me? Please!
Can anyone please help me!?
R_code:
try1<-read.csv("OasisYield1.csv",header=T)
try1$Rate<-factor(try1$Rate)
try1$Block<-factor(try1$Block)
CISER3<-lme(Yield~Treatment+Rate+Treatment*Rate, random = ~1|Block/Treatment,data = try1)
summary(CISER3)
anova(CISER3)
R_output:
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 0.018
R_Code:
test4_HSDpost<-cld(emmeans(CISER3,~Treatment*Rate,type ="response"),tukey="adjust")
test4_HSDpost
R_Output:
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