# Thread: How to calculate P-value?

1. ## How to calculate P-value?

Hi,
i have searched on talkstat and on internet as well but I could find the method of calculating a p-value by hand, all I am getting is p-value calculators.
Can someone kindly explain how do we calculate p-value using z score?
Thanks

2. ## Re: How to calculate P-value?

If you have the z-score, you can calculate the p-value by integration over the normal distribution from -inf to the z-score. Or, you could look it up in z-tables.

here is a graphical representation: http://controls.engin.umich.edu/wiki...ethod:_Z-Score

3. ## Re: How to calculate P-value?

I figured, we have to find the area below the critical value and then subtract from 0.5 and multiply by 2, for two tailed.
Correct?

4. ## Re: How to calculate P-value?

The reason you only find calculators is because the integration Link talks about doesn't have a closed form expression. You literally have to do some numerical analysis to get the value. So technically except for a few choice values we don't actually know what the exact p-value is for a given z-score. We just approximate it to an acceptable accuracy.

5. ## Re: How to calculate P-value?

This series expansion works quite well:

where is the height of the standard normal distribution and when you carry it out until the last terms appears to vanish the absolute error is less than 8X10^-16.

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