# Orange2 Example
# Formulate and test 2-way ANOVA models

# Set colClasses argument in read.table to read
# variety and pesticide as factors.
orange <- read.table("c:/datasets/orange.txt", 
   header=TRUE, colClasses=c("factor", "factor", "numeric"))
print(orange)

# Create and display additive and saturated ANOVA models.
additive <- lm(yield ~ variety + pesticide, data=orange)
summary(additive)
anova(additive)
saturated <- lm(yield ~ variety + pesticide +
   variety*pesticide, data=orange)
summary(saturated)
anova(saturated)

# Create and display null hypothesis models
variety_only <- lm(yield ~ variety, data=orange)
summary(variety_only)
anova(variety_only)
pesticide_only <- lm(yield ~ pesticide, data=orange)
summary(pesticide_only)
anova(pesticide_only)
no_factors <- lm(yield ~ 1, data=orange)
summary(no_factors)
anova(no_factors)

library(car)

# Perform tests of hypothesis by supplying
# two models to anova function: the full model
# and the null hypothesis model

# 1. Test whether interaction is significant.
anova(saturated, additive)
# Conclusion, interaction effect is not significant,
# use additive model.

# 2. Test whether variety is significant
anova(additive, pesticide_only)
# Conclusion, pesticide effect is *** significant.

# 3. Test whether pesticide is significant
anova(additive, variety_only)
# Conclusion, variety effect is *** significant