Completely Randomized Design
Kyle Kenneth Ruaya
2022-12-06
library(readxl)
CRDEqual <- read_excel("D:/Regression Analysis/CRDEqual.xlsx",
col_types = c("text", "numeric"))
CRDEqual## # A tibble: 20 × 2
## Treatment Yield
## <chr> <dbl>
## 1 1.0 25
## 2 1.0 21
## 3 1.0 21
## 4 1.0 18
## 5 2.0 25
## 6 2.0 28
## 7 2.0 24
## 8 2.0 25
## 9 3.0 24
## 10 3.0 24
## 11 3.0 16
## 12 3.0 21
## 13 4.0 20
## 14 4.0 17
## 15 4.0 16
## 16 4.0 19
## 17 5.0 14
## 18 5.0 15
## 19 5.0 13
## 20 5.0 11Fitting of linear model
model <- lm(CRDEqual$Yield ~ CRDEqual$Treatment)
model##
## Call:
## lm(formula = CRDEqual$Yield ~ CRDEqual$Treatment)
##
## Coefficients:
## (Intercept) CRDEqual$Treatment2.0 CRDEqual$Treatment3.0
## 2.125e+01 4.250e+00 -1.410e-15
## CRDEqual$Treatment4.0 CRDEqual$Treatment5.0
## -3.250e+00 -8.000e+00Obtains R square and other statistics of fitted model
summary <-summary(model)
summary##
## Call:
## lm(formula = CRDEqual$Yield ~ CRDEqual$Treatment)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.250 -1.125 -0.250 1.812 3.750
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.125e+01 1.260e+00 16.866 3.67e-11 ***
## CRDEqual$Treatment2.0 4.250e+00 1.782e+00 2.385 0.030702 *
## CRDEqual$Treatment3.0 -1.410e-15 1.782e+00 0.000 1.000000
## CRDEqual$Treatment4.0 -3.250e+00 1.782e+00 -1.824 0.088145 .
## CRDEqual$Treatment5.0 -8.000e+00 1.782e+00 -4.490 0.000432 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.52 on 15 degrees of freedom
## Multiple R-squared: 0.7767, Adjusted R-squared: 0.7171
## F-statistic: 13.04 on 4 and 15 DF, p-value: 8.93e-05Null Hypothesis : All the five treatment means are the same.
Alternative Hypothesis: At least one of the treatment is different.
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 ' ' 1Below 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 ' ' 1print("LSD ANALYSIS")## [1] "LSD ANALYSIS"print(LSD$statistics)## MSerror Df Mean CV t.value LSD
## 6.35 15 19.85 12.69481 2.13145 3.79793print(LSD$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 csink()