st: Re: Test for J or U shaped curve of mean in ordered categories

["Joseph Coveney" <stajc2@gmail.com>]

K Jensen wrote:

I have data that consists of means of a continuous variable in ordered
categories.

How would I test for a J or U shaped pattern in the means?

For testing for a linear trend, I would model the ordinal variable as
a continuous variable in a regression, but that isn't appropriate
here.

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If you have the individual data, or the means, variances (or standard
deviations) and cell counts, then you could still use linear regression with
indicator variables for your ordered categories, and then follow up with a set
of polynomial contrasts to examine nonmonotonicity.  Even for a linear trend, I
would use this classical ANOVA approach over treating the ordered categorical
variable as continuous.

I think that there have been a couple of nonparametric tests, too, for hormesis
in the pharmacology literature, which would be useful if you have access to the
individual data.  I don't know whether they've been implemented in Stata.

Joseph Coveney

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