In article <[EMAIL PROTECTED]>,
Selim Issever <[EMAIL PROTECTED]> wrote:
>I measure a physical quantity about 100 times. I am not interessted in the
>mean value but the spread (the RMS) of this quantity. I can calculate the RMS
>easily, but I also need the error on the RMS. Could you give me a hint how to
>calculate the error on the rms?
To do this roughly: Since you have 100 measurements, you probably know
the mean value fairly exactly. If we considered that the sample mean
is exactly the real mean, then the RMS (ie, the estimated standard
deviation the measurements) is just the square root of the sample mean
of (x-mean)^2. You can get a standard error for this sample mean in
the same way as you get a standard error for any sample mean - by
finding the sample standard deviation of (x-mean)^2 and dividing by
the square root of the sample size. (Of course, this is the standard
error for the RMS^2 - you need to adjust by dividing by 2xRMS to get
the standard error for the RMS itself.)
More elaborately: If you're right that the measurements are Gaussian,
then the distribution of the sample variance (defined with division
by n-1) is that of a Chi-squared random variable with n-1 degrees of
freedom times the variance of the measurements divided by n-1. From
this fact it's possible to get a confidence interval for your estimate
of the standard deviation of the measurements.
Radford Neal
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