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BRAIN TEASER OF THE MONTH

February 15, 2005
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Distinguishing between common sense and dogma: the wisdom of sample size

Dr. Tad E. Gotistic is confident of his ability to instruct the ER nursing staff in the fundamentals of statistical process control (SPC), in spite of the fact that he understands only the use of X-bar and R charts and little else in the way of statistical applications. In any case, he knows that the staff will not understand as much as he does, so that is enough. At least, that had always been enough, when it came to proving his knowledge in a variety of areas.

In the seminar where Dr. Gotistic had learned about charting, the instructor provided an example using 25 samples of 5 each, so this is the approach he uses in his own instruction of the nursing staff. He loves to use the sigma symbol, and is deeply involved in deriving the standard deviation when one of the nurses asks why he has selected a sample size of 5. "Why not 6 or 7, or even 10?" she wonders. This nurse had in fact also once participated in a seminar that offered an overview of SPC, and the instructor had used a sample size of 5 in that case as well.

Dr. Gotistic had a ready answer, asserting that the selection of 5 was required for statistical precision, obliquely suggesting that any other sample size would be flawed in its statistical calculations. "Trust me," he said, "this is statistically sound."

Question:

Why is using a sample size of 5 conventional practice?
a) Dr. Gotistic is right; it is grounded in statistical accuracy.
b) Using a sample size of 5 is the most economical choice.
c) A sample size of 5 renders the arithmetical calculations more convenient.
d) A sample size of at least five creates validity, but there is no magic in 5 itself.

Answer:

c) is correct. Five is the conventional sample size, not because of its link to any statistical principle, but because, as statistician Walter Shewhart pointed out, it makes calculations more convenient. Adding any five numbers and dividing by 5 gives an answer that, by moving the decimal point one place, also provides the average of the numbers.

The control chart, remember, was developed in the 1930s before the $10 calculator or the PC were available for statistical calculations. By the way, don't confuse your kids by announcing this "new" way to calculate the average.

This method works only if the sample size is 5.

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