###R Code for running a multi-factor ANOVA

### Example 1 - Two factors influence gopher tortoise density: Burning and Tree type

###import data

datum=read.csv(file.choose())
head(datum)

### Run multi-factor ANOVA - just list all x variables on right side of equation

results=aov(GopherDens~Treat1+Stand,data=datum)
summary(results) ### Both factors have significant effect

### Run post-hoc test to get estimated differences in groups and confidence intervals
TukeyHSD(results) ### Note that because only 2 groups, p-values are not inflated above t-test

### Run multi-factor ANOVA using LM
results=lm(GopherDens~Treat1+Stand,data=datum)
summary(results) ### Note that confidence intervals and p-values are same as TUKEYHSD
### no multiple tests being run within each factor, no need to control for experiment-wise error rate


### Examples 2 - two factors influence prey density in pitcher plants: mosquitos and decomposing flies

### import data

datum=read.csv(file.choose())
head(datum)

###X variables are numbers, must categorize variables to analyze using ANOVA

datum$MoCat=factor(datum$Mosquitos)
datum$FlyCat=factor(datum$Flies)
head(datum)


### Run multi-factor ANOVA
results=aov(PreyDens~MoCat+FlyCat,data=datum)
summary(results)

### Because multiple groups in each factor, must control for experiment-wise error
### Run Tukeys post-hoc test

TukeyHSD(results)


### Can run Tukey's on just one variable
TukeyHSD(results,"FlyCat") ### Run Tukey's on just FlyCat


### Run multi-factor ANOVA using lm
results=lm(PreyDens~MoCat+FlyCat,data=datum)
summary(results)
### p-values and se don't control for experiment-wise error rate
### no p-value for factor as a whole.

### Examples 3 - multiple regression

results=lm(PreDens~Mosquitos+Flies,data=datum) # Treat x as continuous rather than categorical
Summary(results)