Calculating percentile ranks of a Gaussian distribution

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Discussion Overview

The discussion revolves around estimating the X25, X50, and X90 values of a Gaussian distribution based on test results from a sub-micron particle sizer calibrated with a 1 um (1000 nm) standard. Participants explore the implications of measurement data, the role of standard deviation, and the requirements set by the U.S. Pharmacopeia (USP).

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents test results (X25 = 812.7 nm, X50 = 977.7 nm, X90 = 1389.0 nm) and seeks to find the corresponding percentile ranks for a Gaussian curve with a median of 1000 nm.
  • Another participant questions whether the measurements are from a single particle or multiple particles, suggesting that this distinction is crucial for understanding the data.
  • There is a mention of the USP's requirement that the reference standard values must be within +/- 6% of the test sample values.
  • Some participants express uncertainty about how to estimate the standard deviation of the Gaussian curve based on the provided measurements.
  • One participant notes that the manufacturer typically only provides the median value of 1000 nm and discusses the challenge of estimating the reference standard values without the manufacturer's data.
  • Another participant suggests that the measured values could be the best estimates for the percentiles and questions the assumption that adjusting the X50 value to 1000 nm would improve the estimates.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the estimation of the standard deviation and the implications of the measurement data. There is no consensus on how to proceed with the calculations or the validity of assumptions made about the data.

Contextual Notes

Participants highlight limitations in the available data, including the lack of standard deviation information from the manufacturer and the ambiguity surrounding the nature of the measurements taken.

dwilkerson
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I have been calibrating a sub-micron particle sizer with 1 um (1000 nm) standard.

After testing the standard, the test results on my print-out:

(X25 = 812.7 nm, X50 = 977.7 nm, X90 = 1389.0 nm)

According to USP, the limits are +/- 6% of the reference standard values for X25, X50, and X90.

EDIT: I called the company who made the reference standard and they won't give me these percentile ranks...

Now I've been asked to find the X25, X50, and X90 values of the reference standard Guassian curve that has a median of 1000 nanometers.

I can't seem to figure this out.. Sorry if this is confusing, I can add more information if needed.

Thanks, David
 
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dwilkerson said:
I have been calibrating a sub-micron particle sizer with 1 um (1000 nm) standard.

After testing the standard, the test results on my print-out:

(X25 = 812.7 nm, X50 = 977.7 nm, X90 = 1389.0 nm)

To understand this as a practical problem, it would be necessary to understand whether this printout is a measurement of one particular particle taken many times or whether it is from a set of measurements taken on a large number of particles - or some other combination of different particles and measurements.

According to USP, the limits are +/- 6% of the reference standard values for X25, X50, and X90.

EDIT: I called the company who made the reference standard and they won't give me these percentile ranks...

I, myself, don't know what "USP" means.

Now I've been asked to find the X25, X50, and X90 values of the reference standard Guassian curve that has a median of 1000 nanometers.

It isn't clear what you've been asked to do. Are you to assume that the measurements that you took are good data for estimating the standard deviation of the Gaussian curve for a reference with a median of 1000? An estimate of the standard deviation would let you estimate the whole curve.
 
Stephen Tashi said:
To understand this as a practical problem, it would be necessary to understand whether this printout is a measurement of one particular particle taken many times or whether it is from a set of measurements taken on a large number of particles - or some other combination of different particles and measurements.


The reference standard are polystyrene spheres in a matrix solution. These are diluted in sterile water for injection and measured with laser diffraction instrument (particle sizer). The printout consists of multiple measurements (over the coarse of about 1 minute) from a multiple particles (ref. standard).



I, myself, don't know what "USP" means.


U.S. Pharmacopeia, it's just a huge list of rules for testing chemicals in the medical field. Every year they update their rules.


It isn't clear what you've been asked to do. Are you to assume that the measurements that you took are good data for estimating the standard deviation of the Gaussian curve for a reference with a median of 1000? An estimate of the standard deviation would let you estimate the whole curve.

Usually the manufacturer only gives the median value which is always 1000nm. Now the USP states that reference standard must have x25, x50, and x90 values +/- 6% from the test sample. Since they won't give me their values, I must estimate what the reference standard values are. I'm not sure if there's a way to do this since I don't really have their standard deviation... I know that my printout show 0.225 standard deviation so I could at least use that?
Thanks, David
 
Usually the manufacturer only gives the median value which is always 1000nm. Now the USP states that reference standard must have x25, x50, and x90 values +/- 6% from the test sample. Since they won't give me their values, I must estimate what the reference standard values are

The values you measured are the best estimates you have for those percentiles. If you create another set of numbers by revising the X50 value to be exactly 1000, you are assuming that this improves your estimates because your measuring device has a constant bias. Do you really think that's the case?
 

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