Confidence Limits for a Standard Deviation

In Section 1.3.2, confidence limits are calculated to define a confidence interval within which the true value p is expected with an error probability of p or less. 

For standard deviations, an analogous confidence interval CI(.9jr) can be derived via the F-test. In contrast to Cl(Xmean), ClCij ) is not symmetrical around the most probable value because by definition can only be positive. The concept is as follows an upper limit, on is sought that has the quality of a very precise measurement, that is, its uncertainty must be very small and therefore its number of degrees of freedom / must be very large. The same logic applies to the lower limit. s/  

The true standard deviation Ox is expected inside the confidence interval CI(5 , ) = /Vi. .. /V with a total error probability 2 p (in connection with F and x P taken to be one-sided). 

Thus with a probability of 90% the true value E Sx) - is within the limits 1.2 CTj 3.0. For a depiction of the confidence limits on Sx for a given set of measurements and a range of probabilities 0.0002 p 0.2, see program MSD, option (Display Standard Deviation). 

F-values can be calculated according to Section 5.1.3 and x -values according to Section 5.1.4 (see also programs MSD and CALCVAL) both could also be looked up in the appropriate tables. 

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