Z-score to Percentile Rank Formula?

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SUMMARY

The discussion centers on converting z-scores to percentile ranks using Excel. The user inquires about a formula for this conversion rather than relying on lookup tables. The recommended functions for this task are NORMDIST and INVNORM. Additionally, the discussion highlights the necessity of understanding the underlying calculations, specifically the error function (erf), which is essential for numerical integration over a Gaussian function, as detailed in Abramowitz and Stegun's Handbook of Mathematical Functions.

PREREQUISITES
  • Understanding of z-scores and their significance in statistics
  • Familiarity with Excel functions, specifically NORMDIST and INVNORM
  • Basic knowledge of Gaussian distributions
  • Awareness of the error function (erf) and its applications
NEXT STEPS
  • Research the mathematical derivation of the error function (erf)
  • Explore advanced statistical functions in Excel, including NORM.S.DIST
  • Study the numerical methods for calculating integrals over Gaussian functions
  • Read Abramowitz and Stegun's Handbook of Mathematical Functions for deeper insights
USEFUL FOR

Statisticians, data analysts, and Excel users seeking to automate the conversion of z-scores to percentile ranks while understanding the underlying mathematical principles.

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I was wondering, is there a formula that converts a given z-score to its respective percentile rank? I know I can look up the conversion in a table, but I have a lot of data, and would rather just program a formula into Excel. Obviously, there is some sort of way that whoever created the table made the table, and I'm hoping I can use such a formula.

Thank you!
 
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look up NORMDIST and INVNORM
 
Thanks! That obviously works, but I would hate to use something without knowing how it actually works. Do you know the corresponding formula or procedure to actually calculate it by hand, if it were necessary?
 
You have to numerically calculate the integral over a gaussian function. This integral is called error function (erf). There are some routines out there for the calculation. You might have a look at Abramovitz, Stegun, Handbook of mathematical functions.
 

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