For numerical data you have the solution. But it is categorical data, you said. Then life gets a bit more complicated...
Well, first : The amount of association between two categorical variables is not measured with a Spearman rank correlation, but with a Chi-square test for example. Which is logic actually. Ranking means there is some order in your data. Now tell me which is larger, yellow or red? I know, sometimes R does perform a spearman rank correlation on categorical data. If I code yellow 1 and red 2, R would consider red larger than yellow.
So, forget about Spearman for categorical data. I'll demonstrate the chisq-test and how to choose columns using combn(). But you would benefit from a bit more time with Agresti's book : http://www.amazon.com/Categorical-Analysis-Wiley-Probability-Statistics/dp/0471360937
set.seed(1234)
X <- rep(c("A","B"),20)
Y <- sample(c("C","D"),40,replace=T)
table(X,Y)
chisq.test(table(X,Y),correct=F)
# I don't use Yates continuity correction
#Let's make a matrix with tons of columns
Data <- as.data.frame(
matrix(
sample(letters[1:3],2000,replace=T),
ncol=25
)
)
# You want to select which columns to use
columns <- c(3,7,11,24)
vars <- names(Data)[columns]
# say you need to know which ones are associated with each other.
out <- apply( combn(columns,2),2,function(x){
chisq.test(table(Data[,x[1]],Data[,x[2]]),correct=F)$p.value
})
out <- cbind(as.data.frame(t(combn(vars,2))),out)
Then you should get :
> out
V1 V2 out
1 V3 V7 0.8116733
2 V3 V11 0.1096903
3 V3 V24 0.1653670
4 V7 V11 0.3629871
5 V7 V24 0.4947797
6 V11 V24 0.7259321
Where V1 and V2 indicate between which variables it goes, and "out" gives the p-value for association. Here all variables are independent. Which you would expect, as I created the data at random.