Calculating P-Values From Z-Scores

Question

[Diana]

Hi everyone!

Can anyone tell me how to calculate p-values from z-scores in R? Is this the correct way:

pvalue = pnorm(-abs(z))

Thanks!!!

Answer 1

[Manu Prestat]

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 ;-)

[Diana]

Thanks! my test is one-sided as I am looking at enrichment only

[Emre]

In one-sided case, one is interested to find how extreme is the observation compared to random expectation. Therefore, it seems to be ill defined as it fails to take into account the sign of the z-scores:

pnorm(abs(0.5)) == pnorm(abs(-0.5))

Answer 2

[Gjain]

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.

[Manu Prestat]

You talked about that to your friends!! When are you on holidays Gjain?! :-P

[Gjain]

holidays?? I do not understand Manu ... One of my friend who works on Drosophila had the same query this morning and he asked me how to do that in excel and i told me him that I am more comfortable with R.

[Gjain]

Hi Manu, its been sometime i have been on holiday...One of my friend who works on Drosophila had the same query this morning and he asked me how to do that in excel and i told me him that I am more comfortable with R ...

[Diana]

That is very informative. Thanks Gjain!

Answer 3

[Emre]

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);
}

Answer 4

[Kevin Blighe]

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

Kevin