# R Analysis of a Two-Factor Study (Case II: Interaction Present)  

# We examine the Melon data used for the example from class.  

# Save the data file into a directory and 
# use the full path name:

melon.data <- read.table(file = "z:/My Documents/teaching/stat_705/melondata.txt", 
header=FALSE, col.names = c('fung', 'concen', 'percent'))

# attaching the data frame:

attach(melon.data)

# Making "fung" and "concen" factors:

fung <- factor(fung)
concen <- factor(concen)

# Fitting the ANOVA model and producing the ANOVA table:

melon.fit <- lm(percent ~ fung + concen + fung:concen);
anova(melon.fit)

# We see that a significant FUNG*CONCEN interaction is present (P-value=0.0163).  

# ###############################################################*  

# Tukey simultaneous CIs and hypothesis tests  

# The TukeyHSD function does the Tukey multiple comparison procedure in R. 
# The last column gives the ADJUSTED P-values.  Using alpha=0.05 for the 
# experimentwise error rate, any pair of means with P-value LESS THAN 0.05
# in that column are judged to be significantly different by Tukey.                                                                                                 
# WITH interaction, the pairwise differences in mean response are calculated for all   
# pairs of factor level combinations:  

tapply(percent, fung:concen, mean)

# This produces pairwise differences in mean response for all factor level combinations.  

# Assuming significant interaction between fung and concen, we can use familiar code but 
# we may look at the output marked $fung:concen for comparing ALL factor level combinations using Tukey:                                                
TukeyHSD(aov(melon.fit),conf.level=0.95)

# The table shows the P-values for comparison among all factor level pairs.    
# These P-values below each t statistic are adjusted for the Tukey procedure.  

# conf.level=0.95 is actually the default level.  We could choose  
# another level if desired.    

                                          

# ##################################################################*  

# Estimating and Testing about Constrasts in the Presence of Interaction  

my.interaction <- fung:concen          

# The different combinations are B:100, B:1000, C:100, C:1000, T:100, T:1000                
# This can be seen by looking at:

levels(my.interaction) 

# This will affect how we specify the interaction effects of interest.  

# This is our example from class:  Is the difference between fungicides  
# B and C the same regardless of the concentration? 
contrasts(my.interaction) <- matrix(c(1, -1, -1, 1, 0, 0), nrow=6, ncol=1)
summary(lm(percent ~ my.interaction))
# Look on line labeled 'my.interaction1' for P-value of t-test about this contrast.

contrasts(my.interaction) <- matrix(c(1, 0, -1, 0, 0, 0), nrow=6, ncol=1)
summary(lm(percent ~ my.interaction))
# Look on line labeled 'my.interaction1' for P-value of t-test about this contrast.