Re: Normal Probability Plot... Z-Score Computation

It's a delightful approximation that began with a very simple version
and has been improved over the years. Some tinkering here... adding a
little twist there... and behold. OMU

On Jan 24, 7:19 pm, HopefulProdigy <i...@xxxxxxxx> wrote:
Ok, so the deal is, my AP Stat class went back for a day to review normality assessments (We've just completed P and T hypothesis tests).
One of the assessment possibilities is to make a "Normal Probability Plot" of the data. I completely understand how it works, and how the x value is what the Z-score for that point would have been had the distribution been normal.
But no one knew how that score was calculated. So online I found:

***
The normal probability value z for the jth value (rank) in a variable with N observations is computed as:
z = invNorm [(3*j-1)/(3*N+1)]
***
(http://www.statsoft.com/textbook/glosn.html)

(invNorm being the inverse normal cumulative distribution function, converting probability into z)

This works amazingly accurately when compared to the z-scores of the normal probability plot.
The only thing is that I don't understand how [(3*j-1)/(3*N+1)] calculates the normal probability.
I see that it does in fact fairly accurately find it, but I don't understand why.

So the bottom line is, can anyone explain to me,
"How, and why, does [(3*j-1)/(3*N+1)] fairly accurately predict the normal probability of a data point in a data set?"

.