On Sun, 2 Jan 2000 12:17:13 -0800, "bkamen" <[EMAIL PROTECTED]>
wrote: [ by the way, please set your Output to something
OTHER than HTML. ]
bk>
" This practical question arose between myself and a colleague at
work. It concerns whether we can use correlation analysis if one of
the variables is non-continuous or "categorical." She believes that
both variables must be continuous. However she cannot say why, and I
cannot find any such constraint in the statistics book I have relied
on since graduating in Industrial Engineering a few years ago, Miller
and Freund, 'Probability and Statistics for Engineers.' "
- a Pearson product moment correlation between two dichtomies is
valid and usable, and was called a "phi coefficient" back in the days
when it was useful to have simplified computation formulas for the
easier, special cases. The test on the same 2x2 table using
chisquared (equal to phi-squared times N) is only very slightly
different from the p-value for r, or using an F-test for the derived
t-test. There are not a lot of different ways to account for
variance, so the tests come out the same.
If your *categories* are not (at least) ordered, then a coefficient
of linear relationship is not the appropriate one. It is better that
they are ordered, and with approximately equal (in some sense)
intervals.
bk>
" I have been thinking that if x is discrete and can assume only a few
values compared with y which is continuous, the correlation study may
yield a high probability of type-one error. I interpret this as
providing insufficient evidence with which to reject the null
hypothesis. But I have not thought of this as an inappropriate use of
correlation. " [ snip, rest ]
If you have *outliers*, continuous or discrete, then the test may have
that kind of error. With outliers, the test on r will be more
accurate if you pretend that you have fewer degrees of freedom --
sometimes, just a couple DF despite a large N.
The Cohen/Cohen book on Applied Multiple Regression/Correlation might
be helpful for perspective on r and R-squared.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
