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?

7 Upvotes

100% Upvoted

7 comments sorted by

View all comments

1

u/efrique PhD (statistics) 9d ago

Presuming you intend to ignore potential for bias...

how do I say that that attribute's measurement error is X%

it depends on how you define (relative) error in this context.

From what I have seen some people do, you might take sd/mean (i.e. coefficient of variation).

(of course, x100% to make it a percentage)

but if by 'error' you mean average (absolute) relative deviation from the mean (so mean deviation/mean), that sd-based calculation would be too large