install.packages(“rmarkdown”)

# Set seed that determines the random number generator
set.seed(48183130)  #use your student ID instead of 12345678

# creates data for your homework
i<-c("A","A","A","A","A","B","B","B","B","B","C","C","C","C","C")
table<-as.data.frame(i)

table$X <-as.numeric(ifelse(table$i=="A",round(rnorm(5,mean=5,sd=2),0),
             ifelse(table$i=="B",round(rnorm(5,mean=15,sd=2),0),
              ifelse(table$i=="C",round(rnorm(5,mean=10,sd=2),0),""))))
table

##    i  X
## 1  A  6
## 2  A  7
## 3  A  4
## 4  A  2
## 5  A  4
## 6  B 15
## 7  B 16
## 8  B 17
## 9  B 15
## 10 B 14
## 11 C  7
## 12 C 10
## 13 C  8
## 14 C  9
## 15 C  8

# results for ANOVA test
results<-aov(X~i,data=table)  
summary(results)

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## i            2  300.1  150.07   70.34 2.36e-07 ***
## Residuals   12   25.6    2.13                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# boxplot
boxplot(table$X ~ table$i, main = "Boxplot", xlab = "Group", ylab = "X")

# calculates eta2 and omega2
meanX <- mean(table$X)
meanA <- mean(table$X[table$i == "A"])
meanB <- mean(table$X[table$i == "B"])
meanC <- mean(table$X[table$i == "C"])

sst <- sum((table$X - meanX)^2)
ssb <- sum(5*(meanA - meanX)^2 + 5*(meanB - meanX)^2 + 5*(meanC - meanX)^2)
ssw <- sst - ssb

n <- length(table$i)
dft <- length(table$i) - 1
dfb <- length(unique(table$i)) - 1
dfw <- length(table$i) - length(unique(table$i))
msb <-  ssb/dfb
msw <- ssw/dfw

eta2 = ssb/sst
omega2 = (ssb - (dfb*msw))/(sst + msw)

eta2

## [1] 0.9214081

omega2

## [1] 0.9023993