#Fitting of linear model Ho:African tall=Co-11=FS-1=K-7=Co-24, Ha: Atleast one variety is different

library(readxl)
YieldFile <- read_excel("C:/Users/leocint/Desktop/Leocint/4th Year College(1st Sem.)/Experimental Design/Activities/7/YieldFile.xlsx", 
    col_types = c("text", "text", "numeric"))
View(YieldFile)
model <- lm(YieldFile$Yield~ YieldFile$Replication+YieldFile$Variety)

#Obtain ANOVA

anova <-anova(model)
anova
## Analysis of Variance Table
## 
## Response: YieldFile$Yield
##                       Df Sum Sq Mean Sq F value  Pr(>F)  
## YieldFile$Replication  3  80.80  26.934  0.9205 0.46033  
## YieldFile$Variety      4 520.53 130.133  4.4476 0.01958 *
## Residuals             12 351.11  29.259                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The result above shows the degrees of freedom, sum of squares, mean sum of squares, f value of replication and variety. The * in 0.01958 indicate that varieties are significantly different from each other at 0.05 level of significance. Hence, we will reject the null hypothesis and accept the alternative hypothesis. This means that at least one of the five varieties is different from the rest.

#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)

The plot above will help us check whether the assumption of anova is fulfilled or not. That is, errors are normally distributed.Now, looking at the Normal Q-Q plot, it can be seen that majority of the observation is located in the line or on the line and only few are not. So, the assumption for normality is fulfilled.

Below are the tests used to compare the lines. #Duncan test

library(agricolae)
DNMRT <-duncan.test(YieldFile$Yield,YieldFile$Variety,12,29.259)
DNMRT
## $statistics
##   MSerror Df   Mean       CV
##    29.259 12 31.275 17.29547
## 
## $parameters
##     test            name.t ntr alpha
##   Duncan YieldFile$Variety   5  0.05
## 
## $duncan
##      Table CriticalRange
## 2 3.081307      8.333639
## 3 3.225244      8.722927
## 4 3.312453      8.958792
## 5 3.370172      9.114897
## 
## $means
##              YieldFile$Yield      std r  Min  Max    Q25   Q50    Q75
## African tall          30.450 7.403378 4 22.9 39.1 25.150 29.90 35.200
## Co-11                 31.200 2.762849 4 29.5 35.3 29.575 30.00 31.625
## Co-24                 25.550 5.674798 4 20.4 31.8 20.925 25.00 29.625
## FS-1                  28.475 3.155287 4 24.4 32.1 27.550 28.70 29.625
## K-7                   40.700 6.274286 4 32.1 47.0 38.700 41.85 43.850
## 
## $comparison
## NULL
## 
## $groups
##              YieldFile$Yield groups
## K-7                   40.700      a
## Co-11                 31.200      b
## African tall          30.450      b
## FS-1                  28.475      b
## Co-24                 25.550      b
## 
## attr(,"class")
## [1] "group"

The result above shows the information after applying duncan test in the observation. It can be seen that variety K-7(with ‘a’) is significantly different from the rest of the varieties Co-11, African tall, FS-1, Co-24(with ‘b’).

#LSD test

LSD <-LSD.test(YieldFile$Yield,YieldFile$Variety,12,29.259)
LSD
## $statistics
##   MSerror Df   Mean       CV  t.value      LSD
##    29.259 12 31.275 17.29547 2.178813 8.333639
## 
## $parameters
##         test p.ajusted            name.t ntr alpha
##   Fisher-LSD      none YieldFile$Variety   5  0.05
## 
## $means
##              YieldFile$Yield      std r      LCL      UCL  Min  Max    Q25
## African tall          30.450 7.403378 4 24.55723 36.34277 22.9 39.1 25.150
## Co-11                 31.200 2.762849 4 25.30723 37.09277 29.5 35.3 29.575
## Co-24                 25.550 5.674798 4 19.65723 31.44277 20.4 31.8 20.925
## FS-1                  28.475 3.155287 4 22.58223 34.36777 24.4 32.1 27.550
## K-7                   40.700 6.274286 4 34.80723 46.59277 32.1 47.0 38.700
##                Q50    Q75
## African tall 29.90 35.200
## Co-11        30.00 31.625
## Co-24        25.00 29.625
## FS-1         28.70 29.625
## K-7          41.85 43.850
## 
## $comparison
## NULL
## 
## $groups
##              YieldFile$Yield groups
## K-7                   40.700      a
## Co-11                 31.200      b
## African tall          30.450      b
## FS-1                  28.475      b
## Co-24                 25.550      b
## 
## attr(,"class")
## [1] "group"

The result above shows the information after applying LSD(Least Significant Test) test in the observation. It came up with the same result with duncan on MSerror, Df, Mean, and CV. It also add another information on t value= 2.17881 and LSD= 8.333639. It is visible that variety K-7(with ‘a’) is significantly different from the rest of the varieties Co-11, African tall, FS-1, Co-24(with ‘b’).

#Save the file in txt

sink("YeildFile.txt")
print(anova)
## Analysis of Variance Table
## 
## Response: YieldFile$Yield
##                       Df Sum Sq Mean Sq F value  Pr(>F)  
## YieldFile$Replication  3  80.80  26.934  0.9205 0.46033  
## YieldFile$Variety      4 520.53 130.133  4.4476 0.01958 *
## Residuals             12 351.11  29.259                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
print("DNMRT Result")
## [1] "DNMRT Result"
print(DNMRT$statistics)
##   MSerror Df   Mean       CV
##    29.259 12 31.275 17.29547
print(DNMRT$groups)
##              YieldFile$Yield groups
## K-7                   40.700      a
## Co-11                 31.200      b
## African tall          30.450      b
## FS-1                  28.475      b
## Co-24                 25.550      b
print("LSD Result")
## [1] "LSD Result"
print(LSD$statistics)
##   MSerror Df   Mean       CV  t.value      LSD
##    29.259 12 31.275 17.29547 2.178813 8.333639
print(LSD$groups)
##              YieldFile$Yield groups
## K-7                   40.700      a
## Co-11                 31.200      b
## African tall          30.450      b
## FS-1                  28.475      b
## Co-24                 25.550      b
sink()