August 2002

Vol. 4, No. 8

Quality Quiz from Professor Cleary

You're right!


Responding off the top of his head is generally a mistake for Bjorn Luzer, and this is no exception. He needs to go back to the library for more understanding. He's correct in noting that the numbers both go up, but he's dead wrong about the reasons.
While Bjorn's intuitive response was wrong, the correct answer is consistent with most intuitive understanding of the relationship between sample size and d2. The formula for estimated sigma

clearly represents a ratio of the average range (r-bar) to a weighting factor (d2). One way to look at this ratio is to examine the ways in which R-bar would change as the sample size increases. The value of R is determined by taking the largest number in a sample and subtracting it from the smallest value:
              R = Xlargest    Xsmallest
Imagine selecting a sample size of 2 from a population and calculating the range, then taking a sample size of 5 from the same population and calculating the range for that sample. Which would be larger?
One would expect that the sample size of 5 would offer a greater opportunity for extreme values. In turn, the R-bar is merely the sum of the ranges, so one would expect R-bar to be larger as the sample size increases. Thus d2  becomes larger as n increases, to compensate and to accurately predict the estimate of sigma.


Copyright 2002 PQ Systems.

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