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I am using a hypothetical case to explain my question

Let us consider a chemical analysis method A (using a certain instrument), which is used to quantify the value of a particular species b. According the instrument manufacturer's notes, the instrument used needs to be calibrated once a month. I am analyzing several samples of b in the duration of a month, and using the same calibration curve to obtain the quantity of b along with the uncertainty bound for the value.

I want to understand the following,

  1. If number of samples (over the period of a month) of b are using the same calibration curve to quantify it value, are their errors/uncertainties correlated (by any means, the calibration curve introduces it, however small it may be) ?
  2. Additionally, method A has the ability to quantify several species (b, c, d,$\dots $), does errors/uncertainty of species from the same sample (containing different species like b, c,$\dots$) correlated in any way?
  3. If there exists even a very small correlation, does it make sense to consider it for any further analysis?

I am new to the realm of chemistry (analytical chemistry to be precise), I request your help.

Thank you.

PS: Apologies if the tags are inaccurate

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    $\begingroup$ 1.) Of course, 2.) very likely, but you need to be a lot more specific about A, 3.) how would you do that? You need to have a superior analytical method to only find that correlation. $\endgroup$ – Karl Dec 4 '20 at 6:17
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    $\begingroup$ You should distinguish between errors and uncertainties. If your calibration is somehow systematically wrong (an error has been introduced while determining the relation between observable and expected values) then all values subsequently derived from that calibration will suffer from the same systematic error. This does not mean that the uncertainties due to noise are otherwise correlated. $\endgroup$ – Buck Thorn Dec 4 '20 at 7:07
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Please note that calibrating an instrument once a month is another story as compared to constructing the calibration curve from that instrument. The former is meant to check the accuracy of the instrument's output and the latter serves to determine the concentration of a substance by noting the response of the instrument to 6-7 standards.

Also note that all instrumental analysis techniques are relative with very very few exceptions (gravimetry, microwave spectroscopy, coulometry which are absolute etc.). The rest all need standards for comparison.

In analytical chemistry, it will be considered a bad practice to make a calibration curve one day and use it for the entire month. The good practice is to make a fresh calibration curve for every batch of samples and there should be a "reference" check which keeps on validating the calibration curve after a certain number of samples have been analyzed.

The main reason is that most instruments will show what is called as the drift i.e., a low frequency and hence long term noise in the baseline. The baseline response can rise and decline slowly.

Also the word correlation is perhaps not suitable in your situation. Correlation has a very specific meaning in signal processing/instrumental analysis. What you imply is the influence of interferences and something called as the matric effect. Suppose, you have b, along with c,d,e,...,f. Yes, the presence of the additional components can indeed influence the signal of b. In most cases, the signal of b is decreased causing a lower result than expected.

Beyond your hypothetical situation, one can say nothing. Which instrument you had mind?

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