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### Topic: Relative Standard Deviation  (Read 24493 times)

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#### mir

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##### Relative Standard Deviation
« on: December 05, 2008, 08:05:15 AM »
Relative Standard Deviation (RSD %) is the standard deviation divided by the mean multipluied with hundred.

When you have a series of responses lets say in mV:
x = 12.15  S=0.13
RSD % = 0.13/12.15*100% = 1.06%

From this dataset of responses a series of concentrations was calculated from a calibration curve.
My logic tells me I can apply the RSD % from the response data to the calibrated data without any more worries. But just to be sure, what do you think?

Both data are under the influence of the same random error. But if the two datasets are independent from each other, but the level of noise is the same, can I still apply the RSD % from the responses (above) to concentrations, if the method I used is the same and no other bias is influencing the data?
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#### ARGOS++

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##### Re: Relative Standard Deviation
« Reply #1 on: December 06, 2008, 10:02:46 AM »
Dear mir;

Sorry!,  - Your logic tells you the wrong, also as we don’t know how low your n is.

On the other hand as long as the values for the RSD are low, as yours, it may hold as a first approximation and you have not too much to worry about.

But why?:
For the explanations you have to keep in mind:
-   that SD is the square root (sqrt) of the variance, and only variances are additive.
-   that in real we should correct SD/RSD for low n by the “Student-Factor”
For your calibration you did two observations, the concentration and the mVolts. And as I’m quite sure you declared your concentrations as errorless, so you incorporated the variance into the variance of your mVolts and so your SDcalibr contains both errors.
But for concentration estimations you do always a third observation, the one for mVolts, that means that your total variance will increase by a third term, but will not be doubled as explained above.
As the SD/RSD is the sqrt, the situation looks even less dramatic, and that’s why for low SD’s you have not very much to worry about.
More dramatically would be, if we correct your RSD by the “Student-Factor” for low n’s.

I hope to have been of some help to you.
Good Luck!
ARGOS++
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