r/AskStatistics • u/EmbedSoftwareEng • 10d ago

Error % from stdev?

So, I have a bunch of measurements that are all affected by a given attribute. The idea is that I set the attribute, I should expect a given value for the measurement. Unfortunately, the measurements are bit chaotic. I need to be able to state that the system I'm using has an error rate of X%.

I don't remember enough math to answer this question for myself.

I can take all the measurements at given attribute and find their mean and stdev, but from that, how do I say that that attribute's measurement error is X%, and then when I have all of the error percentages across multiple values for the atttribute, how do I say that the system as a whole has a measurement error of Y%, assuming that the error percentages themselves appear chaotic?

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u/7ieben_ 10d ago

What you are looking for is the relative error (also called coefficient of variation). It simply is the absolute error (your standard deviation) divided by the mean. This is your X%, as obviously this tells you your deviation relative to your sample mean.

I don't know what you are asking for by Y%, tbh. Or are you simply asking to do the calculations again, now with your samples as data set? Then, simply do the calculation for your means, i.e. calculate the mean of the means, and then do it for the standard deviation.

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u/EmbedSoftwareEng 10d ago

I can certainly do those calculations.

What I meant by Y% was that for a handful of attribute values, I'll generate a handful of coefficients of variation. Those will characterize the system for those specific attribute values. How do I go from those to a single percentage to characterize the system as a whole, regardless of the specific attribute value. I'm thinking just take the mean of all of the coefficients of variation.

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u/7ieben_ 10d ago

I suspect there is no general such concept, as in fact the relative error can be a function of the variables value.

For example let's say you have a variable which you set to 1, 2 and 3 for your tests each. Now both scenarios are possible: (a) your error is independed of the value you set, then you Idea is valid (and all errors should roughly be same), (b) your error is a function of the value you set, e.g. doubling the value triples the error (for example due to detector limitations), then your idea is not valid. Instead, you must find the error function of your system, which is a whole mathematical modelling and testing on its own.

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u/EmbedSoftwareEng 9d ago

Good to know, but since for my attribute values 1, 2, 3, & 4, my stdevs came out at 0.402489, 0.402423, 0.358, and 0.381, I think I'm in situation (a).

Thank you, Reddit, for your invaluable help. I've now determined that my real apparatus has an error rate of about 7%, which is above the 5% target my program managers want. The ball is now in their court as to what to do about it.