Anova test

path <- "C:/Users/91999/OneDrive/Documents/Gradedata.csv"
gradedata <- read.csv(path,header = T, sep=",")
View(gradedata)

names(gradedata)

## [1] "Marks" "Grade"

boxplot(gradedata$Marks ~ gradedata$Grade, las=1, ylab= "Marks", xlab="Grade", main="Grade by marks")

aov(gradedata$Marks ~ gradedata$Grade)

## Call:
##    aov(formula = gradedata$Marks ~ gradedata$Grade)
## 
## Terms:
##                 gradedata$Grade Residuals
## Sum of Squares         7494.964   542.000
## Deg. of Freedom               3        24
## 
## Residual standard error: 4.752192
## Estimated effects may be unbalanced

Anova1 <- aov(gradedata$Marks ~ gradedata$Grade)

summary(Anova1)

##                 Df Sum Sq Mean Sq F value   Pr(>F)    
## gradedata$Grade  3   7495  2498.3   110.6 3.45e-14 ***
## Residuals       24    542    22.6                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

attributes(Anova1)

## $names
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "contrasts"     "xlevels"       "call"          "terms"        
## [13] "model"        
## 
## $class
## [1] "aov" "lm"

Anova1$coefficients

##      (Intercept) gradedata$GradeB gradedata$GradeC gradedata$GradeD 
##         94.14286        -13.28571        -27.42857        -44.00000

summary(Anova1)

##                 Df Sum Sq Mean Sq F value   Pr(>F)    
## gradedata$Grade  3   7495  2498.3   110.6 3.45e-14 ***
## Residuals       24    542    22.6                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

TukeyHSD(Anova1)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = gradedata$Marks ~ gradedata$Grade)
## 
## $`gradedata$Grade`
##          diff       lwr        upr     p adj
## B-A -13.28571 -20.29300  -6.278424 0.0001289
## C-A -27.42857 -34.43586 -20.421281 0.0000000
## D-A -44.00000 -51.00729 -36.992710 0.0000000
## C-B -14.14286 -21.15015  -7.135567 0.0000557
## D-B -30.71429 -37.72158 -23.706995 0.0000000
## D-C -16.57143 -23.57872  -9.564138 0.0000054

plot(TukeyHSD(Anova1))

plot(TukeyHSD(Anova1), las=1)

kruskal.test(gradedata$Marks ~ gradedata$Grade)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  gradedata$Marks by gradedata$Grade
## Kruskal-Wallis chi-squared = 25.345, df = 3, p-value = 1.308e-05