Testing the significance of a vector of correlation coefficients using r

Question

I have a vector of correlation coefficients (r) and a vector containing numbers of observations (n), and I want to test each of them to see whether they significantly differ from 0.

r = c(.69,.32,.75,.69,.42,.53,.25,.27,.1,-.15,.48,.39)
n = c(41,233,44,44,44,44,217,217,217,217,217,217)

##### t-values
rt <- function(r,n){
cbind(r/(sqrt((1-r^2)/(n-2))),
n)
}

rt(r,n)

Calaculating the t-values is easy, but is there a way to test them using R, rather than resorting to tables in the back of your stats book?

Answer 1

As to not letting my question stay unanswered, this is how i finally solved it. Thanks to @user20650 for providing the solution!

    r = c(.69,.32,.75,.69,.42,.53,.25,.27,.1,-.15,.48,.39)
    n = c(41,233,44,44,44,44,217,217,217,217,217,217)

    rPV = function(r,n,dec = 8){
        # calculate t-values
        rt <- function(r,n){
            t.value = abs(r/(sqrt((1-r^2)/(n-2))))
            return(t.value)
        }
        t.value = rt(r,n)
        df = n-2
        CDF = round(pt(t.value,df = df),dec) # find location of t-values on the student t-distribution (quantiles). 
        p.value = round(1-pt(t.value, df = df),dec) 

        return(cbind(r,n,df,t.value,CDF,p.value))
    }

    rPV(r,n)

Having this solution, I'd rather recommend calculating confidence intervals than p-values in the end -- they do require some transformation, but allow you to set the confidence level in advance, as well as being ultimately easier to interpret.