After searching on the web without success, I'm asking for help here. I wasn't taught statistics, and I get lost in a lot of formulas that I often find hard to understand. I'm also not used to posting on a forum, let me know if I need to change anything, or give more details!
I'm following a protocol to get the performance of an algorithm. I have measured its average performance X_sample_mean (arithmetic mean) on a population of n samples. I'd like to calculate a confidence interval to estimate the range within which the true mean may be found. I followed the classic method of calculating uncertainty using the Student distribution, described in slide 10 of this link.
This seems to work well, as you can see here the normal distribution associated with my measured mean X_sample_mean, and those associated with the uncertainty (here for a 95% confidence interval): result_confidence_interval
My problem is: I need to work with an RMS (root mean square) instead of an arithmetic mean. Do you know please if this uncertainty calculation remain valid if I simply replace this arithmetic mean value with the RMS value I've measured? If not, how can I obtain the confidence interval associated with this RMS?
Thanks to those who read me.