Randomized Complete Block Design
Winelyn Pelias
2022-12-05
library(rmarkdown)library(readxl)
Yield <- read_excel("D:/Stat 55/Yield.xlsx")
paged_table(Yield)Ho: African tall=Co-11=FS-1=K-7=Co-24, Ha: Atleast one variety is different
Fitting of linear model
model <- lm(Yield$Yield~ Yield$Replication+Yield$Variety)
model
Call:
lm(formula = Yield$Yield ~ Yield$Replication + Yield$Variety)
Coefficients:
(Intercept) Yield$Replication Yield$VarietyCo-11 Yield$VarietyCo-24
29.195 0.502 0.750 -4.900
Yield$VarietyFS-1 Yield$VarietyK-7
-1.975 10.250 Obtain ANOVA
anova <-anova(model)
anovaAnalysis of Variance Table
Response: Yield$Yield
Df Sum Sq Mean Sq F value Pr(>F)
Yield$Replication 1 6.30 6.300 0.2072 0.65592
Yield$Variety 4 520.53 130.133 4.2806 0.01808 *
Residuals 14 425.61 30.401
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The replication was non-significant so the mean yield for all the four replications is same. The treatment was significant i.e. yield of at least on variety is different from the rest. As treatment is significant we should switch to multiple mean comparison test like LSD or DNMRT test.
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 assumptions of ANOVA are not violated.
Load the agricolae package
library(agricolae)Warning: package 'agricolae' was built under R version 4.2.2Duncan test
DNMRT <-duncan.test(Yield$Yield,Yield$Variety,12,29.259)
DNMRT$statistics
MSerror Df Mean CV
29.259 12 31.275 17.29547
$parameters
test name.t ntr alpha
Duncan Yield$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
$means
Yield$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
$groups
Yield$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"Same as the LSD test as both shows same set of sequence of letters.
LSD test
LSD <-LSD.test(Yield$Yield,Yield$Variety,12,29.259)
LSD$statistics
MSerror Df Mean CV t.value LSD
29.259 12 31.275 17.29547 2.178813 8.333639
$parameters
test p.ajusted name.t ntr alpha
Fisher-LSD none Yield$Variety 5 0.05
$means
Yield$Yield std r LCL UCL Min Max Q25 Q50
African tall 30.450 7.403378 4 24.55723 36.34277 22.9 39.1 25.150 29.90
Co-11 31.200 2.762849 4 25.30723 37.09277 29.5 35.3 29.575 30.00
Co-24 25.550 5.674798 4 19.65723 31.44277 20.4 31.8 20.925 25.00
FS-1 28.475 3.155287 4 22.58223 34.36777 24.4 32.1 27.550 28.70
K-7 40.700 6.274286 4 34.80723 46.59277 32.1 47.0 38.700 41.85
Q75
African tall 35.200
Co-11 31.625
Co-24 29.625
FS-1 29.625
K-7 43.850
$comparison
NULL
$groups
Yield$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 variety K-7 gives highest yield with is significantly different from the rest of the varieties. The performance of variety Co-11 was statistically at par with African tall, FS-1 and Co-24.
Save the file in txt
sink("RBD.txt")
print(anova)Analysis of Variance Table
Response: Yield$Yield
Df Sum Sq Mean Sq F value Pr(>F)
Yield$Replication 1 6.30 6.300 0.2072 0.65592
Yield$Variety 4 520.53 130.133 4.2806 0.01808 *
Residuals 14 425.61 30.401
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print("DNMRT Result")[1] "DNMRT Result"print(DNMRT$statistics) MSerror Df Mean CV
29.259 12 31.275 17.29547print(DNMRT$groups) Yield$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 bprint("LSD Result")[1] "LSD Result"print(LSD$statistics) MSerror Df Mean CV t.value LSD
29.259 12 31.275 17.29547 2.178813 8.333639print(LSD$groups) Yield$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 bsink()