Forgive me if this has been discussed already, but I think it hasn't. My class and I discovered today that when MINITAB draws "modified" box plots it identifies outliers by some rule other than the 1.5 x IQR's from Q1 and Q3 that Moore and McCabe and others use. (We got an oulier on the MINITAB plot that didn't show up on somebody's TI-83.). Does anybody know what criteria MINITAB uses to identify outliers? I couldn't find the answer in the documentation (this is Student Minitab for the Mac, v.8, BTW).
----- End of forwarded message from Timothy Brown -----
I am not familiar with this particular version of Minitab, but traditionally Minitab has used the 1.5XIQR rule for detecting outliers. However, it computes the IQR by subtracting the first quartile from the third. Despite what they say, this is not what Moore and McCabe do. Use "describe" on your data and see if you and Minitab agree on Q1 and Q3.
Minitab approaches quartiles using a general approach that fits all kinds of quantiles -- deciles, percentiles, etc. In this system, Q1 has rank 0.25(n+1) and Q3 has rank 0.75(n+1). You can see that this could involve interpolating one-fourth or three-fourths of the way between adjacent data values, while this could never happen with the procedure used in Moore and McCabe.
When Tukey invented the boxplot he used approximate quartiles which he called "hinges". He wanted simple techniques that could be implemented quickly without any computing machinery. Minitab could use these hinges and get boxplots exactly like Tukey's, or it could take the position that hinges are only approximations to quartiles, and so quartiles are the thing to use and Tukey's handmade boxplots are only approximations to the "correct" ones Minitab produces. They seem to have taken the latter position.
Later, the QLP materials implemented a DIFFERENT approximation to the quartiles, and TI implemented this on the grounds that it was what teachers were familiar with. The confusion caused by QLP's introduction of non-standard definitions and conventions has been a pet peeve of mine for some time. It might be interesting to go back over the history of this list and see how many questions have their roots here.
_ | | Robert W. Hayden | | Department of Mathematics / | Plymouth State College | | Plymouth, New Hampshire 03264 USA | * | Rural Route 1, Box 10 / | Ashland, NH 03217-9702 | ) (603) 968-9914 (home) L_____/ email@example.com fax (603) 535-2943 (work)