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Article #3561

Re: Correlation with categorical variables

#3561
From: Allan Reese
Date: Mon, 27 Jan 1992 10:07
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> >I have a categorical variable that I wish to correlate with a number of
> >continuous variables.  The categorical variable has four categories (i.e. a
> >firm can be either in category A or B or C or D).  I have been looking

Mike Katten comments
> I think a more appropriate statistic would be something called a
> point biserial coefficient.  I vaguely remember reading about this
> in Nunnally, but I think it was appropriate for continuous-categorical
> analyses.

The Point Biserial Coorelation has come up many times over the years on
the list, so see monthly archives. Kendall and Buckland describe the
origins of biserial correlation thus, "Originally a coefficient designed
to measure the correlation of two quantities, one of which is represented
by a measurable variate, the other a simple dichotomy ... . Later (1909)
Pearson extended the connotation of `biserial' ..."  (Dictionary of
Statistical Terms 4th Ed).

So the question is whether you want to use some calculation proposed at
the start of this century. Just because something has a name, it doesn't
mean it exists (cf. Cox's Sandpiper). The original question needs to be
spelled out in more detail. Are the categories A B C D ordered? What sort
of association (a more general term than correlation) is expected or sought?
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Date:         Mon, 27 Jan 1992 10:07:22 WET
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From:         Allan Reese <R.A.Reese@SEQ.HULL.AC.UK>
Subject:      Re: Correlation with categorical variables
In-Reply-To:  <received 27 Jan 92 08:50:58 via EDU>; from "Mike Kattan" at Jan
              27, 92 3:16 a