Standard deviation of root mean square error

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SUMMARY

The discussion centers on calculating error bars for root mean square (RMS) error time-series. It confirms that the RMS error is not equivalent to the sample standard deviation due to the divisor difference (n-1 vs. n). For large sample sizes, this distinction becomes negligible. Additionally, participants inquire about calculating confidence intervals for RMS values, indicating a need for further exploration in this area.

PREREQUISITES
  • Understanding of root mean square (RMS) error calculations
  • Familiarity with sample standard deviation concepts
  • Knowledge of statistical confidence intervals
  • Basic statistical analysis skills
NEXT STEPS
  • Research methods for calculating confidence intervals for RMS values
  • Explore statistical software tools for error bar generation
  • Study the implications of sample size on standard deviation calculations
  • Review literature on RMS error in time-series analysis
USEFUL FOR

Statisticians, data analysts, researchers in quantitative fields, and anyone involved in time-series analysis and error measurement.

aydos
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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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