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Patient puzzlers for healthcare PQ Systems supports healthcare quality initiatives.

Does kurtosis require immediate hospitalization?

In order to upgrade his credentials, Dr. Art Terial had looked over a continuing education flier that promoted courses of study to advance learning. Noting that a seminar on statistical process control in health care was being offered in Honolulu, while training in communicable disease prevention was scheduled at a rural site in Illinois, Art’s interest in SPC had suddenly been piqued. He had enrolled in the seminar in Hawaii (motivated by his great interest in statistics), and returned with a tan and with newfound understanding of the potential of data analysis in his health care organization.

Art created a histogram from data related to hospital length-of-stay, and has decided to share his chart with members of a staff team, in spite of the fact that it does not reflect a normal distribution. As the chart indicates, the data seems to reflect a high peak on the right side of the data. The histogram has a number of statistics, including kurtosis, and when staff members begin to file into the room for Art’s presentation, one of them asks for the meaning of kurtosis. His response is that kurtosis is a critical statistic applicable to the medical world.

Is he correct? Select one of the following responses:

A) Dr. Terial is correct. Kurtosis is critical to healthcare applications.

B) Kurtosis is a skin condition that requires immediate hospitalization.

C) Kurtosis is a measurement of the peakedness of a data set.

D) A binomial distribution is indicated by the kurtosis statistic.

The correct answer is C.

If you were tempted to give the dermatology response, wait till you hear two more terms: leptokurtic and platykurtic. These describe two different distributions, all part of what is known as kurtosis, the measure of the combined weight of the tails of a distribution in relation to the rest of it. When tails become heavier, the kurtosis value increases; when they are lighter, it decreases. A normal distribution has a kurtosis of 0, and is called mesokurtic (A below). If a distribution is peaked (tall and skinny), its kurtosis value is greater than 0 and it is said to be leptokurtic (No ointments needed.) (B below). If, on the other hand, the kurtosis is flat, its value is less than 0, or platykurtic (C below). The formula is as follows:

Note that some references to kurtosis do not subtract 3, as shown above. SQCpack subtracts 3 in order to make the statistic 0 for a normal distribution.