Conducting ANCOVA in R.
#packages mountingWe need to know whether martians are hostile or not. Theory - tone of communication relates to the hostility metric, but the intelligence level is a linear covariate of the hostility of the martians.
We also want to see if this relationship holds up over 3 time points.
We need an ANCOVA to see if this theory pans out.
When running ANCOVA, try to identify each of the pieces. above we have
response variable - hostility explanatory variable - tone of communication covariate - intelligence
This will help you lay out the model more intuitively.
#using fake data set that we do not have.
#mars <-read.csv("martians.csv", header=T)
#make sure data look ok
#str(mars)
#tone is numeric - change to factor.
#mars$tone <-as.factor(mars$tone)
#head(mars) #check the first six rows
#dim(mars) #check the dimensions of the data setSTEPS FOR ANCOVA
#step 1 is to test for an interaction. If we have an interaction, there is no point in testing for an ANCOVA with main effects.
#you can just run aov with the interaction only - it will still generate main effects with T1 SS, but the interaction is handled the same way.
#model1 <- aov(time1~intelligence*tone, data=mars)
#step 2 explore the residuals
#try the outliers package
# turn residuals into a data frame
### d <-data.frame(res=Res1, tone=mars$tone)
# run cochran.test for outlying variance
### cochran.test(res~tone)
#if you save the results of the initial ANCOVA to an object called model1, you can plot the entire thing, and R will give you diagnostics.
### plot(model1)
#step 3
### run multiple anovas across the three time points, treating them as an independent study.
# IN homework 3, q3, run:
# aov(START~biomass*tissue, data=kelp)
################ NEVER DO THIS IN PRACTICE, UNLESS IT IS PURELY DIAGNOSTIC -
####### TIME CANNOT BE TREATED AS A NUISANCE VARIABLE IN A LONGITUDINAL MODEL
####### MOREOVER, THESE ARE MULTIPLE TESTS THAT ARE NOT ADJUSTED FOR TYPE 1 ERROR INFLATION
# each time, test for interaction first. If it is significant, there is no need to run model version b, because the main effects become irrelevant
#model1a <-aov(Time1~tone * intelligence, data = mars)
#model1b <-aov(Time1~tone + intelligence, data = mars)
#model2a <-aov(Time2~tone * intelligence, data = mars)
#model2b <-aov(Time2~tone + intelligence, data = mars)
#model3a <-aov(Time3~tone * intelligence, data = mars)
#model3b <-aov(Time3~tone + intelligence, data = mars)