Z-score to Percentile Rank Formula?

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Discussion Overview

The discussion centers around the conversion of a z-score to its corresponding percentile rank, exploring both practical applications in programming and theoretical underpinnings of the conversion process.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about a formula for converting z-scores to percentile ranks, expressing a preference for a programmatic solution over using tables.
  • Another participant suggests using the functions NORMDIST and INVNORM as a practical approach for the conversion.
  • A further reply expresses a desire to understand the underlying formula or procedure for calculating the conversion manually, rather than relying on built-in functions.
  • One participant explains that the conversion involves numerically calculating the integral of a Gaussian function, referencing the error function (erf) and suggesting resources for further exploration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single formula for the conversion, and multiple approaches and perspectives are presented, indicating an unresolved discussion.

Contextual Notes

The discussion does not clarify specific assumptions or limitations regarding the methods proposed, nor does it resolve the mathematical intricacies involved in the conversion process.

Who May Find This Useful

Individuals interested in statistical analysis, programming applications in Excel, or the theoretical aspects of probability and statistics may find this discussion relevant.

The Head
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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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