There have been a couple of good posts in response to this question --
and I agree that r is not a desirable statistic, and that it is what
you report when you can't come up with something better -- but I think
I still have something to add.
On Mon, 10 Jul 2000 07:41:15 GMT, Znarf Akfak
<[EMAIL PROTECTED]> wrote:
> I'm considering reporting Pearson's correlation coefficient with a
> confidence interval for several bivariate associations. As bivariate
> normality is assumed under the computation of the confidence interval,
> I have two questions.
>
> 1. What is a good way to examine the assumption of bivariate normality
> for a given data set?
As a start: look at the univariate distributions; and consider the
logical relations. There is apt to be *damaging* violations if there
are distant outliers, or if there are peculiar logical connections
(instead of "linear" associations that should be expected).
> 2. To what extent are such confidence intervals robust to departures
> from bivariate normality?
To what extent? The CIs of an r are less robust than the point
estimates of r . The effect of outliers is that the size of r is
controlled by a small(-er) number of points; so the test, if there is
a fair one created by Monte Carlo simulation, has a smaller number of
"Degrees of freedom" (effectively speaking), and a more extreme
cutoff value for "5% significance"; or, a wider CI.
Departures in the form of "discreteness" don't have much effect.
Incidental (univariate) skewness puts stringent limits on Pearson
correlations between variables, according to the amount that their
skews are shared or opposed.
> References to publications would be much appreciated as I don't have
> access to CIS, as would other suggestions and comments.
>
Tukey, "EDA" Exploratory Data Analysis. Mosteller and Tukey, "Data
analysis and regression."
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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