Accuracy and reproducibility issues

[Sarah1233]

Hi guys

I know that to make sure that your method is accurate you need to repeat your experiment in triplicates, Why the no. 3 why not 2 or 4. Is there any statistical reason for that?

Regards
Sarah

[DSP007]

Hi
Yes of course. three - the minimum number for which a mathematical sense to calculate the standard deviation. And the first number in which a standard deviation or the spread can be found clanger.

[Peter Apps]

Hi Sarah

You are confusing accuracy with precision. When you run multiple replicates the agreement between the results is a measure of the precision, more properly called repeatability of whatever steps you replicated - if you just do multiple injections from one vial you are measuring the repeatability of the instrument, if you prepare three replicate samples you are measuring the repeatability of the method.

Accuracy is a measure of how close the measurement result is to the "true" value. Typically this would be determined by running a sample with a known content of analyte, either prepared in house by spiking an otherwise clean sample, or obtained as a certified reference material.

To get back to your original question; repeatability is expressed as the relative standard deviation (rsd) of the results. The more replicates that you run the more reliable the estimate of rsd becomes (the estimates of rsd themselves have mean, sd, and rsd). Three is the minimum number that gives an acceptably small rsd of the rsd.

Peter

[Alex Buske]

Hi
Yes of course. three - the minimum number for which a mathematical sense to calculate the standard deviation. And the first number in which a standard deviation or the spread can be found clanger.

Three is the smallest number of replicates that allows to calculate a SD. With 2 replicates you just get the difference.
It doesn't make mathematical sense to calculate the SD from 3 values. When we once had a process that produced "challenging" CUT results, we always went for n=30 as the RSDs from n=10 weren't consistent enough.

Doing accuracy with just one replicate is far to susceptible to weighting and dilution errors. With two replicates and two different results you don't know which one is wrong or if it is just the poor reproducibility.
So three replicates is a compromise between security and workload.

[lmh]

accuracy and precision has already been dealt with, so no comment.

About the number of replicates:

The standard deviation is a measure of how much individual measurements vary. The more measurements you make, the more accurate will be your assessment of the standard deviation. But the standard deviation, on average, doesn't get smaller as you make extra measurements. The reason is that each individual measurement is still just as likely to be some distance from the mean.

The standard error, on the other hand, does get smaller as you make more measurements. Standard error is s.d. divided by square root of the number of measurements. It is a measure of how much the currently-measured mean is likely to vary from the "real" value, were you to carry out the whole experiment again, with the same replication.

If you're testing whether result "A" is the same as some particular value (e.g. "A" = "B") then the important thing isn't the error in individual measurements of "A" (i.e. standard deviation), it's the error in your overall estimate of "A" (i.e. the standard error).

If A is likely to differ from B by some huge amount, then small errors in A don't matter. If the difference is small, then for it to be statistically significant, you need a much closer margin of error on your measurement.

For this reason, "3" isn't always the right answer of replicates. "2" is definitely wrong, but 4, 5, 6 and so on might all be right, depending on the expected differences you expect to see between treatments. Three is traditional because it's the cheapest experiment that will still survive a reviewer and have a chance of getting published, but only if you're expecting big changes!

Do a Google search for "Statistical power" for more detail.

[DSP007]

Number of replications depends on the required accuracy of analysis. To recognize the correct result should know how we avoided the admission. For example the tolerance on the content of the drug in tablets of 90 to 110% of par value. Accordingly, if we have two points and two points were in the middle (100%) - all OK. But if the point of getting laid at the edge (89.9, 90.0, 90.2%), then we have to achieve this convergence of results at each stage of the analysis to be exactly sure where we are. So when a very narrow tolerance (for example, in the drug substance may be 99.0-100.5%) - may be required and 10 Parallel to establish as accurately as possible the concentration of titrating solution.

On the other hand - if we need a precision of plus or minus kilometer, for example you need to know if we can find in the mixture which is a substance or a substance we can not find it, it is sufficient and one input.

I fully agree that 3 is chosen for reasons of minimizing the cost analysis in most cases.
Google translate

[Peter Apps]

Number of replications depends on the required accuracy of analysis.

Unless something has been lost in translation, you are also confusing accuracy with precision. You can run as many replicates as you like of an inaccurate (biased) method, and the results will still be biased.

Peter

[DSP007]

OK .
Here nuance automatic translation.

In Russian the meaning of the word [accuratnost] / accuracy/ is less. An example of "a accuracy housewife."
But meaning of the word [tochnost' ] /the accuracy also /is very broad. Example of application - [popal tochno v cel'] "hit exactly in the middle of the target", but on the other hand, ["tak tochno"] "so aptly", that is to be done as said. There is a narrow concept of precision in technical book - an example of "pretsizonno isgotovlennoe" ( manufactured for machining device with high precision in dimension ) "
Finally, the narrow meaning is the concept of convergence and its alternative - the spread , the deviation. For example, [malij razbros] " small devation of bullets " or " good convergence of a series of parallel dimensions."

It is natural that the automatic translation of these details are unknown, replacing the word "tochnost' " of any permutation of the values ​​determined by random computer selection.


The meaning in my reply was as follows.
If you need to shoot in a aircraft balloon - you can take a rifle with the battle worse than if you want to shoot in 10 cent money. Аnd weapons can shoot fewer rounds.
[ In the sense - for to put on the gunpoint corrections to shoot in the ballon , you need to make fewer fired than if we determine the corrections for the shoot in money.] Large scatter of bullets at a larger goal becomes less important.
But for the answed of question "a real rifle or a child's toy?" metrology is not needed. This question solved after shooting the first bullet. Similarly, in chromatography - ask "a method good work or not wok? " "Can we see it matter or not" - solve the first injection and to answer these questions, whithout mathematics.

[Peter Apps]

In English, as in Russian, the ordinary meanings of "accuracy" and "precision" can be different to the technical meanings that should be applied in science. For example; a rifle is said to be accurate if it puts five bullets into a small group on a target. The size of the group is actually a measure of precision (repeatability). The distance between the centre of the bull (the aiming point) and the centre of the group is a measure of accuracy.

"Precision engineering" implies both accuracy and precision - the dimensions have a narrow tolerance (small deviation) around an actual dimension that is a close (precise) match to the specification (low bias).

Taking multiple shots at a target, with either a machine gun or a shotgun increases the probability of a hit, but is wasteful compared to a properly sighted rifle.

May I suggest something concerning the use of automatic translators ? Translate from Russian to English, and then translate back again from English to Russian. If the final Russian version is hard to understand, then the English is probably difficult too.

Peter

[gstaepels]

Hi,

I was asked to run the repeatability of the average molecular weights (Mn and Mw) of a polymer. The technique used is GPC and the calibration is done with polystyrene. Can I just calculate the Standard deviation and the %RSD on the results (in Daltons) or should I first transform them to the logaritmic scale, since the log(M) is a function of the retention time?
Thanks for your comments.