Completely Randomized Design Analysis in R along with LSD

(Reading time 6 min.)
Click here for Data set

R-script

#Fitting of linear model

model <-lm(CRD$Yield ~ CRD$Treatment)

#Obtains R Square and other statistics of fitted model

summary <-summary(model)

#Carryout ANOVA

anova <-anova(model)

anova

#Below codes are used to obtain plots of fitted vs Residuals and Normal QQ plots

par(mfrow=c(1,2))

plot(model, which=1)

plot(model, which=2)

#Load the package

library(agricolae)

#Carry out LSD test

LSD <-LSD.test(CRD$Yield,CRD$Treatment,anova$`Df`[2],anova$`Mean Sq`[2])

#Generate the txt file of analysis

sink("crdanalysis.txt")

print("ANOVA of CRD")

print(anova)

print("LSD ANALYSIS")

print(LSD$statistics)

print(LSD$groups)

sink()

Output 

[1] "ANOVA of CRD"
Analysis of Variance Table

Response: CRD$Yield
                            Df            Sum Sq     Mean Sq         F value    Pr(>F)   
CRD$Treatment  1               220.90       220.900          19.335    0.0003477 ***
Residuals            18              205.65       11.425                     

 

[1] "LSD ANALYSIS"
  MSerror Df  Mean       CV  t.value      LSD
   11.425 18 19.85 17.02815 2.100922 5.021379
 

  CRD$Yield groups
2     25.50      a
1     21.25     ab
3     21.25     ab
4     18.00     bc
5     13.25      c

Click on the image to expand

Interpretation:

From ANOVA: The treatment source has p-value less than 0.01, so it is significant at 1 % level of significance. This means that one or more treatments means are unequal so we reject our null hypothesis of ANOVA Ho: All the five treatment means are the same. Now it's a green signal for multiple mean comparison test like LSD (least significant difference).

From LSD test: Treatment 2 has the highest mean which was at par with Treatment 1 and 3.

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If you are using "agricolae" package for analysis. You can cite it as:

Mendiburu, Felipe. (2010). Agricolae: Statistical Procedures for Agricultural Research. R package version. 1. 1-8. 

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Topics you might be interested in:

Split plot analysis in R

 Degrees of freedom

Principles of designs of experiments-I: Replication

Principles of designs of experiments-II: Randomization

Principles of design of experiments-III: Local control