[R] multiple paired t-tests without loops

[Daniel Malter]

Hi Matt, see the example below. It took me a while to figure it out. I
suggest you carefully examine the example step by step. It computes t-values
for dataset with 3 variables and 8 unique combinations of two binning
variables. The code should extend easily to larger datasets. Also, it uses
the existing variable combinations only once, thereby further gaining
efficiency. If you want a paired t-test, you will have to adjust the t-value
computation in tt.test below (I implemented an unpaired t-test), and the
code cannot handle NAs, which you would have to implement if needed. 

#Simulate data
data=data.frame(
grim=rnorm(100),
flik=rnorm(100,1,1),
prok=rnorm(100,0.5,1)
)

#Create a vector 1 do the number of variables to be tested in your data
#needed for indexing
b=1:length(data)

#Create binning variables that jointly define unique combinations
id1=rep(c(1:4),each=25)
id2=rep(c(1:2),50)

#Get unique combinations of two variable names
comb.a=t(combn(names(data),2))
#same as above for numeric variable indicators
comb.b=t(combn(b,2)) 

#Get unique combinations of the binning variables
comb.id=expand.grid(unique(id1),unique(id2))

#Aggregate data needed to compute t-tests
#for each unique binning variable combination
#i.e., for each row in comb.id
meanss=aggregate(data,by=list(id1,id2),mean)
varss=aggregate(data,by=list(id1,id2),var)
Nss=aggregate(data,by=list(id1,id2),length)

#Define a function for the t-test

tt.test=function(x){
  test.means=meanss[,2+x]
  test.vars=varss[,2+x]
  test.Ns=Nss[,2+x]
 
(test.means[1]-test.means[2])/sqrt(test.vars[1]/test.Ns[1]+test.vars[2]/test.Ns[2])
  }

#Apply the t-test over each row of comb.b
#where the rows in comb.b serve as the
#column indicator x used in tt.test
results=apply(comb.b,1,tt.test)

#Show results
#Results are in order of the eight unique
#combinations of id1 and id2 in comb.id
#presented in blocks for each combination
#of two variables (grim/flik, grim/prok, flik/prok)
results

#Combare the first element of the results
#with the individual t-test of the bin
# id1==1 and id2==1
t.test(data$grim[id1==1&id2==1],data$flik[id1==1&id2==1])

Hope this helps,
Daniel





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