Correlation between numerical and categorical data in R I have a dataset with over 20 variables. Some of them are numerical and some of them are categorical:
C          <- c(4, 8.5, 2, 5, 6)
N          <- c(0.4, 0.1, 0.5, 1.2, 1.1)
moisture   <- as.factor(cbind("dry","dry","dry","wet","wet"))
vegetation <- as.factor(cbind("forest", "wetland", "field", "forest", "wetland"))
df         <- data.frame(C,N, moisture,vegetation)

I want to know the pairwise correlation between each of these variables. I found two solutions for this: rcorr() and hetcor(). While rcorr gives me Pearsons's product-moment correlation or Spearman's rho rank correlation including p-values, hetcor() offers me the discrimination into polyserial and polychoric correlations, but no p-values.
I would use rcorr with Pearson which has the advantage of also including p-values, but I am not sure if it qualifies for this sort of data. Can I still talk of correlations in this case or do I need to talk about significance of association? If I use hetcor I seem to gain the advantage of it being applicable for categorical data, but I don't get the p-values.
 A: From hetcor documentation you can learn that

Computes a heterogenous correlation matrix, consisting of Pearson
  product-moment correlations between numeric variables, polyserial
  correlations between numeric and ordinal variables, and polychoric
  correlations between ordinal variables.

It computes correlation in case where one or two of the variables are ordinal, i.e. categorical where categories can be ordered in a meaningful way. Categories: "forest", "wetland", "field" cannot be ordered (at least I cannot imagine any meaningful way for it). Correlation measures a linear relation (or lack of it) such that one of the variables increases when the other one increases (positive correlation), or one of the variables increases when the other one decreases (negative correlation). There is no increase or decrease between "forest" and "wetland" etc., so you cannot measure such linear relation for categorical variable. See also here for discussion of similar case where order of categories makes a difference.
See also Should types of data (nominal/ordinal/interval/ratio) really be considered types of variables?.
