P-value for polyserial correlation

Question

I have some basic questions concerning the polyserial() {polycor} function.

1. Does a p-value exist for rho, or can it be calculated?
2. For the assumption of a bivariate normal, is the tested null hypothesis "Yes, bivariate normal"? That is, do I want a high or low p-value.

Thanks.

Answer 1

If you form the returned object with:

 polS <- polyserial(x, y, ML=TRUE, std.err=TRUE) # ML estimate

... You should have no difficulty forming a p-value for the hypothesis: rho == 0 using a z-statistic formed by the ratio of a parameter divided by its standard error. But that is not the same as testing the assumption of bivariate normality. For that you need to examine "chisq" component of polS. The print method for objects of class 'polycor' hands that to you in a nice little sentence. You interpret that result in the usual manner: Low p-values are stronger evidence against the null hypothesis (in this case H0: bivariate normality). As a scientist, you do not "want" either result. You want to understand what the data is telling you.