#Input data
sample1 <- c(22,21,19,23,24,22)
sample2 <- c(19,17,19,18)
sample3 <- c(23,26,19,18,20)
alldata <- c(sample1,sample2,sample3)


#Category Totals
sum1 <- sum(sample1)
sum2 <- sum(sample2)
sum3 <- sum(sample3)
allsum <- sum(alldata)

#Optional. If you don't want to count your sample sizes manually, you can automate it using the length() function.
n1 <- length(sample1)
n2 <- length(sample2)
n3 <- length(sample3)
totaln <- n1 + n2 + n3

#SS(between)
ssbetween <- (sum1^2)/n1 + (sum2^2)/n2 + (sum3^2)/n3 - ((sum1 + sum2 + sum3)^2)/totaln
ssbetween


#Also, since we will use it later, you can write
sumx <- sum1 + sum2 + sum3

#SS(total)
sstotal <- (sum(alldata^2)) - ((sum(alldata))^2)/totaln
sstotal

#SS(within)
sswithin <- sstotal - ssbetween
sswithin

#Mean Squares
msfactor <- ssbetween/(3-1)
mserror <- sswithin/(totaln-3)
msfactor
mserror

#F test statistic
fstat <- msfactor/mserror
fstat

#p value (always right tailed). Note, df=k-1 for the numerator, and df=n-k for the denominator
1-pf(fstat,3-1,totaln-3)

#Optional. Critical value
qf(.95,3-1,totaln-3)


mean(sample1)
mean(sample2)
mean(sample3)

#Input data
sample1 <- c(72,84,77,80,81)
sample2 <- c(83,73,84,81)
sample3 <- c(80,78,84,81,86,79,82)
alldata <- c(sample1,sample2,sample3)

#Specify group membership for each x in "alldata"
#This says, the first 5 things belong to group 1, the next 4 things in group 2, and so on
group <- c(rep(1,5),rep(2,4),rep(3,7))

#Put the data into a special object called a ``data frame"
#This is organized like a table, rather than just a list
data <- data.frame(y = alldata, group = factor(group))

#We create a linear model first and then apply the anova() function to it
fit <- lm(alldata ~ group, data)
anova(fit)

#Input data
sample1 <- c(180,183,172,178,169,179,178)
sample2 <- c(185,181,180,179,164,165,180,178)
sample3 <- c(170,183,172,175,164,170,176,167,166)
alldata <- c(sample1,sample2,sample3)

#Specify group membership for each x in "alldata"
#This says, the first n1 belong to group 1, the next n2 things in group 2, and so on
#We get nj = length(samplej)
group <- c(rep(1,length(sample1)),rep(2,length(sample2)),rep(3,length(sample3)))

#Put the data into a special object called a ``data frame"
#This is organized like a table, rather than just a list
data <- data.frame(y = alldata, group = factor(group))

#We create a linear model first and then apply the anova() function to it
fit <- lm(alldata ~ group, data)
anova(fit)