Question 2: The standard deviation of inter-operator differences was 0.56 mm, 0.46 mm, and 0.44 mm, based on using single measurements by each operator and the averages of two and of three measurements, respectively. Why did the standard deviations get smaller as the number of observations increased? The drops in standard deviation are not very large. Why is this?

The variance of these differences is made up of two components: the variance between the operators and the variance of repeated observations by the same operator. If we take the average of two repeated measurements by each operator, the first part remains exactly the same because it is the effect of the operator, but the second part is reduced. It is divided by 2. Hence the variance is reduced by using two measurements, but it is not halved. The standard deviation is correspondingly reduced, but not by as much as it would be if divided by root 2.

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Last updated: 23 February, 2007.