Calculating percentile ranks of a Gaussian distribution

[dwilkerson]

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

 

[Stephen Tashi]

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.

 

[dwilkerson]

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

 

[Stephen Tashi]

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?

 

[blue_raver22]

Dear David,

Calculating percentile ranks of a Gaussian distribution involves determining the percentage of values in the distribution that fall below a certain point. In this case, the X25, X50, and X90 values represent the 25th, 50th, and 90th percentile ranks, respectively.

To find the percentile ranks of the reference standard Gaussian curve with a median of 1000 nanometers, you will need to use the standard normal distribution table. This table provides the percentage of values that fall below a certain number in a standard normal distribution, which has a mean of 0 and a standard deviation of 1.

First, you will need to convert the X25, X50, and X90 values from nanometers to standard deviations by subtracting the mean (1000 nm) and dividing by the standard deviation (6% of 1000 nm = 60 nm). This will give you the values -3.145, -0.371, and 2.315, respectively.

Using the standard normal distribution table, we can find the percentage of values that fall below these numbers, which will give us the percentile ranks for the reference standard Gaussian curve. The percentile ranks for X25, X50, and X90 are approximately 0.1%, 35%, and 99.5%, respectively.

I hope this helps you in your calculations. Let me know if you need any further clarification or assistance.

Best,