P value of corrcoef() is aways different !

Hi, in my tests i've introduced Matlab corrcoef(). But if i repeat this test i'm used to obtain different results for p value. The same thing if i cosider rand() function. So :

t=1:200000;
a=rand(1,200000);
[l,p]=corrcoef(a,t)

first time

l =

    1.0000    0.0016
    0.0016    1.0000

p =

    1.0000    0.4742
    0.4742    1.0000

second time

l =

    1.0000    0.0025
    0.0025    1.0000

p =

    1.0000    0.2729
    0.2729    1.0000

third time

l =

    1.0000   -0.0000
   -0.0000    1.0000

p =

    1.0000    0.9941
    0.9941    1.0000

what is the meaning of these results?

[Jeff Miller]

You seem to be generating new random values of 'a' for each run, so the correlations of those values to 't' (which are returned in 'l') naturally vary randomly as well. Since the correlations vary, so do their associated p values. What aspect of this is surprising to you?

[Damiano Capocci]

Of course correlation varies but i expected a p value more or less the same in each generation and high because we are talking about rand(). I don't have a clear idea about the uniform distribution of p value itself. Ok if the generation is a stochastic variable p value will be also a stochastic variable but....

Answer 1

[the cyclist]

I'll one up you. I ran your code 10,000 times and calculated the P value for each run.

Here's the code:

NT = 10000;

pvec = nan(1,NT);

t=1:200000;
for n = 1:NT

      a=rand(1,200000);
      [~,p]=corrcoef(a,t);

      pvec(n) = p(1,2);

end

figure
histogram(pvec)
title(['Distribution of P values after ',sprintf('%d',NT),' trials'])
xlabel('P')
ylabel('Frequency of occurrence')

Here's resulting the distribution ...

Uniformly distributed P values (with a bit of sampling error). Exactly what I would expect. What were you expecting, and why?

[Damiano Capocci]

I would expect a"decent" p value (or at least more or less the same) for each generation due to the fact we are testing rand() which is a good generator

[the cyclist]

A uniform distribution of the P value is exactly what I would expect from a good generator. The two distributions you are comparing are not correlated. Therefore, you would expect a P value of 0.05 or less to occur 5% of the time. You would expect a P value of 0.1 or less to occur 10% of the time.

This is exactly the result (within sampling error).