Standard deviation S , the square root of pooled variance, may also be used for testing the authenticity of the observations taken in future on a similar instrument.
A criterion may be formulated that the difference between any two observations should not be greater than the standard deviation S or its multiple.
For example, assuming the normal distribution for all observations with S as its standard deviation, then no difference between any two observations should be greater than twice the value of 1.96 times the value of S(95% level of confidence). That is semi-range of variations in observations is ˙1:96 S.
the idea of pooled variance is being used, for routine calibration of weights in Mass Standards activity of National Physical Laboratory, New Delhi, India, for the past so many years.
In a precision balance for a given specific range, the variation in the observations is almost independent of denomination of weights. The standard deviation S from the pooled variance of balance for weights of specific denominations is found out and used as permissible limits for the two mass values obtained for weight of same denomination by two observers under similar environmental conditions. If the difference between the two values is less than 2 S, the mean of the two values is taken and reported as the mass value of the weight piece with S as one component of standard uncertainty evaluated by Type A method. Otherwise the mass value of the weight is redetermined. This is a stricter criterion than suggested in the above paragraph (level of confidence is 66%).
Source of Testing the Authenticity: measurement uncertainty
