Last month’s column, “Beware the Tukey Control Chart,” generated several questions of a fundamental nature that deserve expanded answers. These questions and their answers will be considered here.

Interquartile ranges

The Tukey control chart uses the interquartile range or IQR to characterize dispersion. One statistician wrote that he had found the IQR to be useful, especially in the presence of outliers. While he is right in saying that the IQR is less sensitive to outlying data points than is the global standard deviation statistic, this does not make it an appropriate measure of dispersion for a process behavior chart. The problem with the IQR is that it is a global measure of dispersion, i.e., it uses all of the data in the computation. As a global measure of dispersion it makes an implicit assumption that the data are homogeneous. This assumption is a distinct problem when you are examining the data for evidence of a lack of homogeneity, which is the purpose of a process behavior chart.

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