# p value relationship to standard error as samples increase?

#### redsocks

##### New Member
Hi all,

I would appreciate some help regarding the relationship between the p value and some other elements in my question below. Any help would be appreciated! I've spent about 4 hours researching this, and am still stumped....

How would you calculate the relative size of a p value given the following elements:

p = 0.55 for a 2X2 table

n = 40

odds ratio = X (not given)

If we did the study again with a sample of n = 120 and obtained the same odds ratio, what'd be the relative size of the p value for this new sample?

I am assuming that it'd be smaller, because the more samples = smaller standard error. But how is the p value directly related to the standard error? And how is it that the same odds ratio is found in both samples?

I honestly don't even know what "relative size" means other than to say smaller or bigger than. I've tried looking on the net, and there is a similar unanswered question on this forum, but different.

I'm really stumped, and don't know if this needs algebra or some math expression to calculate.

I'd appreciate anything Many thanks

#### rogojel

##### TS Contributor
hi,
my guess would be the following:

the logarithms of the OR are approximatively normally distributed, so, the p value can be calculated using the z value z = (ln OR -0)/stderror

or spelled out z= ln OR / ( stddev/sqrt(n)).

If we change from n1 to n2 then then it would be easy to calculate the proportion z2/z1 = sqrt(n2/n1)

Calculating the proportions of the p values would be more difficult because the p- values are not linear functions of p.

I hope this helps a bit.
regards

#### redsocks

##### New Member
Hi rogojel,

Thanks very much for your help. I think I really just need to say whether the p value in the second study will be smaller or larger than the first study, and give my reasons why, rather than a calculation (because I don't have the OR value)

Many thanks!