Question

Pringle et al (2015) experimentally examined the effects of fire and herbivory by elephants on the density of geckos that live in trees in Kenya, using 4 ha study plots. They excluded elephants from half of the plots and left the other half unfenced. Then they burned the vegetation in half of the plots and left the other half unburned (see sketch below). Each treatment was replicated once in three different areas used as blocks: Central, North and South. Four months after the treatments were applied, the researchers estimated the density of the gecko species Lygodactylus keniensis in each plot (number of individuals / m2 ).

Block	Elephant Treatment		Fire Treatment	July 2013 lizard density per ha
Central	Elephants present		Burned	853.33
Central	Elephants present		Unburned	183.33
Central	No elephants		Burned	270
Central	No elephants		Unburned	256.67
North	Elephants present		Burned	784.44
North	Elephants present		Unburned	298.89
North	No elephants		Burned	417.78
North	No elephants		Unburned	212.22
South	Elephants present		Burned	661.11
South	Elephants present		Unburned	356.67
South	No elephants		Burned	380
South	No elephants		Unburned	388.89

Using R, calculate the standard deviations of the four treatments

Answer 1

we can rectify the column names of the data as below to enter in R

Block	Elephant.Treatment	Fire.Treatment	lizard.density
Central	Elephants present	Burned	853.33
Central	Elephants present	Unburned	183.33
Central	No elephants	Burned	270
Central	No elephants	Unburned	256.67
North	Elephants present	Burned	784.44
North	Elephants present	Unburned	298.89
North	No elephants	Burned	417.78
North	No elephants	Unburned	212.22
South	Elephants present	Burned	661.11
South	Elephants present	Unburned	356.67
South	No elephants	Burned	380
South	No elephants	Unburned	388.89

In R we can fit the ANOVA as below:

Now we can answer the given questions using above ANOVA table

Answer(a):

The factor “Fire” has 1 degree of freedom

Answer(b):

The factor “elephants” has 1 degree of freedom

Answer(c):

The interaction has 1 degree of freedom

Answer(d):

The block effect has 2 degrees of freedom

Answer(e):

We have 6 degrees of freedom for error.

Answer(f):

The total number of experimental units is 12.

R-code:

data=read.table("clipboard",sep="\t",header=T)
data$Block=as.factor(data$Block)
data$Elephant.Treatment=as.factor(data$Elephant.Treatment)
data$Fire.Treatment=as.factor(data$Fire.Treatment)
data.aov=with(data,aov(lizard.density~Block+Elephant.Treatment*Fire.Treatment))
anova(data.aov)