#
# Exercise 5.1a - continues on from Exercise 4.2
#
# Statistical Methods in Biology: Design and Analysis of Experiments and Regression
# by S.J. Welham, S.A. Gezan, S.J. Clark & A. Mead (2014)
# Chapman & Hall/CRC Press, Boca Raton, Florida. ISBN: 978-1-4398-0878-8
# Data from K. Hammond-Kosack, Rothamsted Research
# Version 1, 26/09/2014

# Set working directory - use setwd() function or from Session menu in RStudio
# e.g. setwd("d:/stats4biol/data)

# Read data 
grains <- read.table("grains.dat",sep="",header=T)
summary(grains)

# One-way ANOVA
grains.aov <- aov(Grains~Treatment, data=grains)
summary(grains.aov)

# Get simple residuals
simple.res <- residuals(grains.aov)

# get standardized residuals
std.res <- rstandard(grains.aov)

# plot standardized against simple residuals
plot(y=std.res, x=simple.res)

# Check whether ratio is constant?
std.res/simple.res

# Check distribution of standardized residuals
hist(std.res)


# Additional material

# Verify SE of simple.res
# Get estimate s^2
grains.aovt <- summary(grains.aov)[[1]]
ResMS <- grains.aovt$"Mean Sq"[2]; ResMS
s2 <- ResMS
# Get replication of treatments
n.table <- aggregate(Grains~Treatment, data=grains, FUN=length)
n <- n.table$Grains[1]; n
# Calculate SE(simple.res)
se.simple = sqrt(s2*(n-1)/n); se.simple
# Check inverse = ratio of std.res to simple.res
1/se.simple

# End of file