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I am running a relatively simple propagation of error analysis on an equation:

$$S = \frac{ABC}{XY}$$

I have independent random error terms calculated for each variable (for the purposes of this analysis I am assuming systematic errors to be negligible), but I am having a specific issue with the $C$ variable in that, after some testing, we are certain that the quantity it represents is being under-represented. Restated, during the data collection process, some data loss is occurring and $C$ represents a numeric quantity and is capturing roughly only 75% of the true value according to our best estimates (which is to say, if we have, say, $C=5$, our data indicates that this is only 75% of the true value of C).

Is there a specific way to deal with this situation? My first inclination is to run some simple algebra and calculate the true value for the variable (in the above example of $C=5$, quick math gives me a "true" value of roughly $C=6.6667$) but I am unsure if this is the best or most rigorous way to go about handling this situation. Any advice or citations to assist would be greatly appreciated.

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  • $\begingroup$ What quantitative information do you have about this "data loss"? What kind of "testing" are you referring to? $\endgroup$ – whuber Jan 7 '13 at 14:15
  • $\begingroup$ The quantitative information amounts to a series of mock trials using a known quantity for measurement to determine how much loss occurs through the measurement process. In other words, we have, say, three grams of a substance measured in a quantity of water in a graduated cylinder. We then perform the same experimental test process with which we normally derive C. From there, we compare the measurement of the added substance to the initial three grams, and determine how much loss has occurred through the test process. Our best estimate for this loss factor is roughly 25%. $\endgroup$ – E P Jan 7 '13 at 15:48
  • $\begingroup$ You should take a look at questions related to calibration. $\endgroup$ – whuber Jan 7 '13 at 17:49
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    $\begingroup$ It looks like the opening three lines and the title (and the tags) misrepresent the actual question here, which doesn't seem to be about error-propagation at all, but dealing with the problem with $C$. Once you have a way of dealing with that, it might lead to a question about how that impacts error propagation, but this doesn't look like that question. $\endgroup$ – Glen_b Sep 5 '13 at 5:01
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You say that the systematic errors are negligible, but the situation you describe with C is a systematic error. However, you know the magnitude of the error, so you correct for it by dividing C by 0.75, which eliminates the systematic error. Now, the uncertainty associated with the 0.75 has to be propagated along with the uncertainty of all the other variables to find the combined uncertainty in S.

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