How to calculate P-value?

[SadieKhan]

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

[Link]

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

[SadieKhan]

Thanks link
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?

[Dason]

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.

[Dragan]

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.