your expression is good. Just don't forget, if relevant, to take into account the two-sided characteristic of the test, it would be then:

pvalue2sided=2*pnorm(-abs(z))

And, if you think you need to use the "apply" function, you might need to think about multitesting correction... but, I agree, this is another topic ;-)

Hi Diana,

I was explaining the same thing to my friend this morning.

Here is a very nice and useful link: Calculating p Values

1. Calculating a Single p Value From a Normal Distribution
2. Calculating a Single p Value From a t Distribution
3. Calculating Many p Values From a t Distribution

I hope this helps.

Based on the previous answers and comments, here is a function that considers both the one-sided case (two alternatives, observed scores are greater / z is positive: "+", observed scores are lower / z is negative: "-") and two sided case ("NULL").

convert.z.score<-function(z, one.sided=NULL) {
    if(is.null(one.sided)) {
        pval = pnorm(-abs(z));
        pval = 2 * pval
    } else if(one.sided=="-") {
        pval = pnorm(z);
    } else {
        pval = pnorm(-z);                                                                                 
    }
    return(pval);
}

Yet another [late] answer, in the context of GWAS: SNP dataset and Z Score

Kevin