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Re: Quartiles (y/n) y
Posted:
Mar 11, 1997 2:58 PM


 Forwarded message from Bob Hayden 
From edstatl@jse.stat.ncsu.edu Tue Mar 11 00:29:03 1997 Received: by oz.plymouth.edu; id AA15544; Tue, 11 Mar 1997 00:26:51 0500 Received: from by jse.stat.ncsu.edu (8.6.11/SL31jan95) id AAA01585; Tue, 11 Mar 1997 00:26:23 0500 Date: Tue, 11 Mar 1997 00:26:23 0500 MessageId: <9703110521.AA17873@oz.plymouth.edu> ReplyTo: hayden@oz.plymouth.edu Originator: edstatl@jse.stat.ncsu.edu Sender: edstatl@jse.stat.ncsu.edu Precedence: bulk From: Bob Hayden <hayden@oz.plymouth.edu> To: Multiple recipients of list <edstatl@jse.stat.ncsu.edu> Subject: Re: Quartiles age? XListserverVersion: 6.0  UNIX ListServer by Anastasios Kotsikonas XComment: Statistics Education Discussion
 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 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (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 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



