Chromatography Forum

Can we calculate the RSD for two values,n=2, statistically/scientifically.

Thanks/ Regards

For two values, we would generally use the % difference instead of RSD:

ABS(Value1-Value2) * 100 / AVG(Value1, Value2)

Dear Tim,

I agree with you, but my question is, if we calculate RSD for n=2, then will it statistically correct? Can any audito object to it?

Thanx/ Regards

I think there is no reason, why you could not calculate the RSD of a duplicate analysis

Regards Bert

%RSD = 100 * standarddeviation/mean

standard deviation (s) = measure of spread of your data.
68% of all your data is within mean±s
95% of all your data is within mean±2s
99% of all your data is within mean±3s

I don't think it's statisticaly significant to determine your s on 2 measurements. You can't talk about data spread if you only have 2 measurements. If you would talk about a difference, use the % difference as stated above.

The FDA guidance for industry, bioanalytical method validation is mentioning the incorporation of QC samples in duplicate at three concentration levels, and evaluation of the precision (RSD) per concentration level.........

So, maybe it depends on what you want to achieve.

Regards Bert

FDA guidance for industry Q2B validation of analytical procedures:
http://www.fda.gov/cber/gdlns/ichq2bmeth.pdf

p8: 5. Precision: 5.1 Repeatability
Repeatability should be assessed using:
(1) A minimum of 9 determinations covering the specified range for the procedure
(e.g., 3 concentrations/3 replicates each); or
(2) A minimum of 6 determinations at 100 percent of the test concentration.

Bartjoosen,

the number of replicates you mention, are used in the proces of validation. The question was, whether it is meaningfull to calculate the RSD of a duplicate

Regards Bert

The FDA guidance for industry, bioanalytical method validation is mentioning the incorporation of QC samples in duplicate at three concentration levels, and evaluation of the precision (RSD) per concentration level.........

So, maybe it depends on what you want to achieve.

Regards Bert

Indeed the question was, wether it is meaningfull to calcultate the RSD of a duplicate. I answered that question some replys ago.

It looks to me that you have answered with a guidance for validation.
I replied only your answer with the link I found about the FDA guidance for analytical procedure validation.

This is indeed offtopic.

But if I wasn't clearly enough:
I don't found it meaningfull to calculate the RSD of a duplicate

Jumping in here,

ajaib5's question involved "would an auditor object". If dealing with pharmaceuticals, the answer is "yes".

Is an RSD calculation from two values meaningful, the answer is "not really". In any standard deviation calcuation, what you are doing is estimating the population standard deviation from the standard deviation of your sample runs. When you have only two runs to work with, this estimate has so much slop that it is virtually meaningless.

In short, there is a reason why validation requires so many replicates.

It looks to me that you have answered with a guidance for validation

The referred guidline also discusses the use of QC samples when a method is in use in real life. So, in that case, an auditor can't object. But maybe, it all depends on what your doing, pharmaceutical or bio-pharmaceutical analysis??

Ajaib5, are you dealing with pharmaceuticals?

Regards Bert

I had some time today, and I have done some calculations:
I calculated the %RSD for 2 measurements (95%-105%): 7.07%
But also the Confidence interval: 3.15 - 225.6

When I perform 3 measurements (95-100-105)
this becomes: %RSD: 5; CI 2.6 - 31

As you can see the confidence interval decreases with the increasing number of measurements.

I think it's important to make up for yourself what am I going to do with this data. How important is the accuracy of the %RSD?

If its just to see the %difference between 2 measurements, you can calculate %RSD for this, it will give you an idea of spread, but mathematicaly the basic use of the standard deviation becomes useless.

But how many time you calculate the 95% confidence interval for you assay results?.....

Kind regards

Bart

The EP has in 2.2.46 a table quoting RSDs from up to 3 single values.
It really depends on what you use the RSD for. For validations the guideline define minimum requirements and for CUTs the pharmacopoeias.
From my experience it is sufficient (normally distributed values):
-for a mean value 2-3 single values, each additional value will add certainty, but will not change the mean value very much. RSD can differ from determination to determination.
-for the "process" RSD 6 values should be the minimum, often even 7th, 8th or 9th value changes the RSD. after 10 the RSD has "leveled in", I wouldn't expect to big changes anymore.

Alex

I agree with Mr. Tom Jupille.

Based on Remington’s Pharmaceutical Science, we could find these statements:
There are 2 measurements of variation: the range and the standard deviation.
The range is most valuable in small series of observation, usually for n less than 10. For n greater than 10, the standard deviation gives a much better estimate of the variation than the range. The two are quite closely related, especially for sample sizes less than 10. When n=2, the range and the standard deviation are equally as efficient.