Completely Randomized Design

library(readxl)
CRDEqual <- read_excel("D:/COLLEGE 4TH YEAR/1st SEMESTER/STAT 55 EXPERIMENTAL DESIGN/MIDTERM/CRDEqual.xlsx", 
    col_types = c("text", "numeric"))
CRDEqual

Fittinf of linear model

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

Obtains R square and other statistics of fitted model

summary <- summary(model)

Carryout ANOVA

anova <- anova(model)
anova

Analysis of Variance Table

Response: CRDEqual$Yield
                   Df Sum Sq Mean Sq F value   Pr(>F)    
CRDEqual$Treatment  4 331.30  82.825  13.043 8.93e-05 ***
Residuals          15  95.25   6.350                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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

par(mfrow=c(1,2))
plot(model, which = 1)
plot(model, which = 2)

Carry out LSD test

library(agricolae)

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

$statistics
  MSerror Df  Mean       CV t.value     LSD
     6.35 15 19.85 12.69481 2.13145 3.79793

$parameters
        test p.ajusted             name.t ntr alpha
  Fisher-LSD      none CRDEqual$Treatment   5  0.05

$means
    CRDEqual$Yield      std r      LCL      UCL Min Max   Q25  Q50   Q75
1.0          21.25 2.872281 4 18.56446 23.93554  18  25 20.25 21.0 22.00
2.0          25.50 1.732051 4 22.81446 28.18554  24  28 24.75 25.0 25.75
3.0          21.25 3.774917 4 18.56446 23.93554  16  24 19.75 22.5 24.00
4.0          18.00 1.825742 4 15.31446 20.68554  16  20 16.75 18.0 19.25
5.0          13.25 1.707825 4 10.56446 15.93554  11  15 12.50 13.5 14.25

$comparison
NULL

$groups
    CRDEqual$Yield groups
2.0          25.50      a
1.0          21.25      b
3.0          21.25      b
4.0          18.00      b
5.0          13.25      c

attr(,"class")
[1] "group"

Generate the txt file of analysis

sink("CRDEqualanalysis.txt")
print("ANOVA of CRDEqual")

[1] "ANOVA of CRDEqual"

print(anova)

Analysis of Variance Table

Response: CRDEqual$Yield
                   Df Sum Sq Mean Sq F value   Pr(>F)    
CRDEqual$Treatment  4 331.30  82.825  13.043 8.93e-05 ***
Residuals          15  95.25   6.350                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

print("LSD ANALYSIS")

[1] "LSD ANALYSIS"

print(LSD$statistics)

  MSerror Df  Mean       CV t.value     LSD
     6.35 15 19.85 12.69481 2.13145 3.79793

print(LSD$groups)

    CRDEqual$Yield groups
2.0          25.50      a
1.0          21.25      b
3.0          21.25      b
4.0          18.00      b
5.0          13.25      c

sink()