Chromatography Forum

Our lab currently calculates amounts (with excess precision) for individual injections of each sample prep in Emower2 then calculates the average amount of all injections for each sample prep. We are transferring a method to another lab that averages the responses (with excess precision) of individual injections of each sample prep then determines what they call the average amount for each sample prep. Does anyone have a reference (or a sound statistical argument) which way is better or are they equally acceptable? Thanks in advance for your input.

It don't think it would make any difference, but why not try it both ways and see if you get the same answer?

Tom, you are too kind.

I feel what you are doing is better, but there's not a lot in it. Reasons are the following:

If you are measuring something in ng, you want to know the error in ng. If your calibration curve is absolutely linear, the percentage error in peak area is the same as that in amount, but if the curve is not absolutely linear, then you'd need to calculate the error in ng using the calibration curve, which is extra work, and I can't think of a chromatography data system that would do it.

Extreme example to illustrate the problem: if your detector is totally at its maximum, the precision on peak areas may be very good (all peaks are identical, maximum!). The precision on peak height will be phenomenally good. But the precision on amount is totally dreadful because over a wide range of amounts, all answers are equal...

Less extreme, if you're using a detector that curves off a little, the percentage error on peak area will be less than that on amount (if you can get away with it, you could use this to pull a fast one and claim better precision than you have).

Yes, you may have a linear detector and a method that is validated over a linear range, but I don't feel comfortable with the idea of building data-handling methods into my lab that hold hidden hazards if they are later applied to a method or detector that isn't so obliging.

Thanks to everyone who posted.

Tom we did this and yes they are different (that's why I'm here) but looking further into the raw results they are different not because of averaging pre- or post- calculation, but rather because of differences in rounding performed by each group. In Empower, we try to use as many custom fields as possible in order to have every parameter available to perform many different calculations. We also assign precision to each calculation custom field based on the calculations involving the actual parameter(s) then add (as allowed by SOP) an additional defined precision (because this is "intermediate rounding" otherwise) to continue with the calculation(s), and also we can hand verify any calculation. The Client uses Excel and also puts in each variable independently but uses full precision (so they cannot be accused of performing "intermediate rounding") for all calculations than rounds at the end. We can't reproduce their numbers with their data and they can't reproduce our numbers with our data each using our own calculation scheme. We can reproduce each labs results when we do the calculations the same way. This rounding error is within the acceptance criteria for assay but occasionally fails (depending on the magnitude of concentration) for the impurity results, especially near LOQ levels.

However, I was trying to be polite and find a way to suggest to the Client that another way of calculating their results might be better (not to say our way is the better way!!).

IMH made the point about detector response being less sensitive (in the usual linear ranges) than the concentraiton and perhaps averaging the response may hide something, and by this fault, averaging concentration would be better. Although even IMH is convinced that this isn't a very strong argument over the averaging of concentrations.

So I gues I'll have to live with rounding errors (like most of us do). I'll consider this topic closed. Thanks, again everyone.

Hi Kevin

If two methods of rounding (or rounding vs not) give different reported results then there must, by definition be something wrong with the rounding.

Of course, if you are doing the calculations with long strings of extra decimals that cannot be justified by the precision of the measurements themselves you will see differences in the numbers far to the right, but these should be rounded away when you report your results anyway.

The ISO Guide to Uncertainty of Measurement has the definitive guidance on how rounding needs to relate to the required uncertainty of the reported results.

Peter

Thank you Peter for your reply.

I did not intend this topic to go into a discussion about rounding per se, as I'm sure every poster/reader here has their own story about reounding issues. You are correct there are guidances out there on rounding (I haven't read the ISO guide, but I have read the EURACHEM guide). Most of the compaines I've worked at have a SOP on rounding which dictates how it is suppose to be performed. And in fact, most auditors (for the pharmaceutical industry which my company is in) expect such an SOP to be in place and that it is followed.

Your points are well taken and I agree, that precision must be defined by the measurement and not the capabilites of the computer/calculator. But, perhaps, some of the older SOPs on rounding don't appreciate the current capabilites of the data systems currently in use and thes SOPs need to be updated to more accruately reflect the artifical precision these systems produce. Your are also correct that the rounding errors at the 15th decimal place is not the issue. The issues are closer to the second or third decimal place espcially for impurities that have concentrations of < 0.1 % (typically the case).

Thanks again for your comments.

Hi Kevin

What you get by extending strings of numbers is not precision (which is a measure of how closely the results of repeated independent measurements agree) but resolution aka readability. Nearly all modern instruments have readability that is higher than the precision of the methods that are run on them - in practice if you run replicates you want to see at least the last decimal changing so that you can be sure that the readability extends beyond the precision.

If, for arguments sake, you weigh single figure grams of sample on a typical 4-figure analytical balance you have 5 significant figures - if you then analyse that sample and get a peak area with 12 figures the last 7 of them are spuriously high resolution.

This spurious resolution has been around for a long time - those little HP integrators that used narrow thermal paper gave peak areas with great chunks of spurious resolution tacked onto the end.

For your impurities determinations - if different rounding procedures change the results then perhaps you have too little readability rather than too much.

Peter

Hello Peter and thanks again for your reply.

I wholly concur with your discussion, and yes I do remember the HP printers with the 2" thermal tapes.

"Readability" or "artificial precision" we agree on the concept if not on the words. And you are right, it is due to too little "readability" on our part, but we intentionally did this to more correctly reflect true precision of the individual parameters.

Thanks,
Kevin

Just a thought...
If your two areas are close, does it matter?
If your two areas are widely different, averaging the responses could hide this OOS, calculating each result to an amount and then averaging would flag alerts.

(might have missed the point here... but FDA are looking for traceability to the base data.)

Are you rounding before averaging? IIRC that shouldn't be done. Rounding should be used at the end to represent the actual precision, but should never be done in the intermediate steps.

If I recall correctly....


Edit: Derp derp...just read your previous post thoroughly, yeah you are pretty clear that you aren't doing intermediate rounding.


Edit2:
While you're stating that there is no intermediate rounding the differences in results sound almost exactly like what you would get from that. The only other cause would be a different precision in a constant used or a flat out calculation error.

If you are doing some system of

[A]+ = [C]
Avg ([C]) = F1

Avg([A]) + Avg () = F2

then with proper handling of precision these values should be identical. Unless you either have a rounding issue going on, or....if someone is tossing out outliers in earlier steps. I think..... you would have to hold off on dismissing any outliers until you got to the F1/F2 step. Don't know if that applies.

This will depend on the calculation.

See if this works/helps: If you have somethign of the form y = m*x and several vaues of x, you can compute y for each x or compute the mean value for x and from that compute the mean value for y. But this works as long as m is constant for each x. If there is an addtional term such as adding in a sample weight, then this may not work.

If I look at y = x1/m1 + x2/m2 + x3/m3, I can not take the average of the x terms and divide by the average of the m terms. I must find a common denominator. (Working the division of each x/m fraction takes care of that - making the denominator 1) So if I am looking for recovery per sample weight and have mg recovered from the chroatographic analysis (mg/extract) and samples are close but not exactly the same in weight (g/sample), I must work the recovery for each sample (mg (per extract)/g (sample weight)) - then I can average them.

It has been many years since middle school -- and finally I am beginning to make sense of word problems! I think.