# Relationship between effect size, sample size and p-value?

#### KelvinS

##### New Member
Is there a simple formula that links effect size, sample size and p-value?

Specifically, how does the p-value depend on effect size and sample size? Are there any other critical factors involved in this relationship?

I'm basically looking to understand how these factors are linked mathematically, via a formula... any ideas?

K.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Standard error is important in most tests. It is your measure of sample variation and incorporates the n-value (sample size) . It gets used in the denominator of statistical tests and the calculation of confidence intervals in frequentist approaches.

#### KelvinS

##### New Member
Thanks, I guess I already knew that. But mathematically, how are these factors all linked? What does the formula look like?

#### rogojel

##### TS Contributor
hi,
I think you should look at the power calculations for a given test. Most formulae are numeric, even in simple cases, but you get a link between the sample size, effect size and the probability that p will be below a threshold. ( generally 0,05)

regards

#### KelvinS

##### New Member
Are you saying there is no formula to calculate an expected p-value given a particular effect size and sample size? No way to express it mathematically, even if numerical methods are involved???

I find this very hard to believe.

I can understand why many people are lazy and prefer to blindly use software that does these calculations in a black box, without understanding what's actually going on ... but still, there *must* be some mathematical relationship that underpins these calculations. Statistics is not voodoo!

#### Karabiner

##### TS Contributor
p values are determined using a test statistic (r, F, t, Chi² etc.)
and its particular distribution. The value of the test statistic in
a given analysis is calculated using the data pattern in the sample.
Determination of a p-value from the test statistic often takes into
account sample size, but not always (Chi²).

Effect size, in contrast, is a concept related to populations, not
to samples. Effect size plays no role when the p value is
determined from sample data.

With kind regards

K.

#### KelvinS

##### New Member
Thanks Karabiner.

So in that case, what is the relationship (formula) between the p-value, correlation coefficient (r or phi), and sample size n?

And how can this relationship/formula be extended to look at correlations between multiple (k>2) variables?

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#### Karabiner

##### TS Contributor
Do you mean something like what is discussed here ?

With kind regards

K.

#### KelvinS

##### New Member
Possibly, but I can't see how that links p to n and r, especially when there are multiple variables that are correlated together.