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Topic: Re: Quartiles (y/n) y
Replies: 0

 Bob Hayden Posts: 2,384 Registered: 12/6/04
Re: Quartiles (y/n) y
Posted: Mar 11, 1997 2:58 PM

----- Forwarded message from Bob Hayden -----

From edstat-l@jse.stat.ncsu.edu Tue Mar 11 00:29:03 1997
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Date: Tue, 11 Mar 1997 00:26:23 -0500
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From: Bob Hayden <hayden@oz.plymouth.edu>
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Subject: Re: Quartiles age?
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----- Forwarded message from Terry Moore -----

Tukey divides the data into two groups using the median. He counts
the median in both groups when there are an odd number of data
whereas Moore & McCabe leave it out of both groups. Both
conventions then take the medians of the groups as the hinges.
I don't know why Tukey did this - it doesn't generalise to
thirds (and Tukey uses thirds for his Rline method) or to other
partition values.

One method is to use 0.25 (or 0.75 or other proportions)
*(n+1) where n is the sample size and count this number of
observations, interpolating if it is not an integer.

----- End of forwarded message from Terry Moore -----

The last of these is what Minitab does for quartiles (as given by
DESCRIBE) but it uses Tukey hinges to make boxplots.

Generally, Tukey's EDA methods were designed to be done quickly
without computing machinery, so interpolating 0.75 or 5/12 (as one
paper recommends), would not be viable choices. That's why they are
"hinges" rather than quartiles. His choice has for me the
metaphysically satisfying property that the five number summary of a
batch of five numbers consists of the numbers themselves. The other
methods would summarize five numbers with artificial constructs.
Doing this, or worrying about consistency with other -tiles is very
Platonic, while data analysis is profoundly Aristotelian.

_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College MSC#29
| | Plymouth, New Hampshire 03264 USA
| * | Rural Route 1, Box 10
/ | Ashland, NH 03217-9702
| ) (603) 968-9914 (home)
L_____/ hayden@oz.plymouth.edu
fax (603) 535-2943 (work)

----- End of forwarded message from Bob Hayden -----

--

_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College MSC#29
| | Plymouth, New Hampshire 03264 USA
| * | Rural Route 1, Box 10
/ | Ashland, NH 03217-9702
| ) (603) 968-9914 (home)
L_____/ hayden@oz.plymouth.edu
fax (603) 535-2943 (work)