# Bret Larget
# April 27, 2009
# ANOVA Analysis of fat data, Evans and Rosenthal Example 10.4.1

# Response is grams of fat absorbed while cooking donuts
# There are eight different types of fat
# There are six observations per treatment group

# Read in the data
fat = read.table("fat.txt",header=T)

# Plot the data separately for each treatment group
library(lattice)
print( xyplot(absorbed ~ type, data=fat, pch=16) )

# Can also make side-by-side boxplots
print( bwplot(absorbed ~ type, data=fat) )

# Things to notice from the graphs:
# (1) While the sample means are different in each group,
#     it is less clear if the differences can be explained by chance alone.
# (2) The variability within each group is about the same.

# Here are some numerical summaries.
# Note the use of tapply() to apply a function separately to each part of the variable absorbed
# that is partitioned by the factor type.

fat.mean = with( fat, tapply(absorbed,type,mean) )
fat.sd = with( fat, tapply(absorbed,type,sd) )
print(cbind(fat.mean,fat.sd))

# Use lm() to fit a linear model (ANOVA)

fat.lm = lm(absorbed ~ type, data=fat)

# Print out the estimated coeeficients
print(summary(fat.lm))

# Print the ANOVA table

print(anova(fat.lm))