Standard deviation of root mean square error

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The discussion focuses on calculating error bars for root mean square (RMS) error time-series, with an emphasis on understanding the relationship between RMS error and standard deviation. It clarifies that RMS deviation is not the same as sample standard deviation due to the different denominators used in their calculations, though this difference is negligible for large samples. The conversation also shifts to inquiries about calculating confidence intervals for RMS values. Participants seek references to support their findings in academic writing. Overall, the thread highlights the nuances of statistical measures in the context of RMS error analysis.
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I am comparing two RMS error time-series and I would like to generate error bars on the RMS results. I think the RMS error is a standard deviation of an assumed zero mean process, and I have the gut feeling that this should be the standard deviation of the sample standard deviation. Is that correct? I would like to have a reference to cite on a paper I am writing at the moment, so if anyone knows of a useful reference I would appreciate some pointers.
Thanks in advance.
 
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RMS deviation about the mean is not exactly the sample standard deviation because in computing the sample standard deviation you divide by n-1 instead of n. For large enough samples the difference is not important.
 
Hi mXSCNT,
Yes thanks for pointing that out. The sample sizes are large.
How about the confidence intervals of the RMS values? Any clues in how to calculate them?
 

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