|
I'm not sure if it is power, or absolute relative efficiency, in which nonparametric tests clearly outperform parametric tests when parametric assumptions are not met. As far as elegance, does anyone know the source of the following?
"Parametric tests are exact solutions to approximate problems, nonparametric tests are approximate solutions to exact problems."
Michael T. Scoles, Ph.D.
Associate Professor of Psychology & Counseling
University of Central Arkansas
Conway, AR 72035
>>> "Marc Carter" <[EMAIL PROTECTED]> 9/28/2006 10:39 AM >>>
Hey, Chris --
I could be wrong about this, but most of what I've seen comparing power of the two sorts of tests has come from Monte Carlos and bootstrapping methods for generating a distribution based on the data. I don't know that there's a way to _a priori_ compute the power of a non-parametric test.
But again, I could be wrong, and welcome correction if I am.
And it's good that you note that people still (unjustifiably) underestimate the power of non-parametric tests. They're actually pretty nifty and will get the right answer almost all the time. They're often not perceived as being as mathematically "elegant" as parametric tests, and I think we have a bias against them.
Cheers,
m
-------
"Mauchly's Test of Sphericity:
Tests the null hypothesis that the error covariance matrix of the
orthonormalized transformed dependent variables is proportional
to an identity matrix."
---
SPSS
I cannot tell you how to calculate the power of nonparametric tests, but I am certain that one can, because there is an extensive scholarly literature comparing the relative powers of nonparametric tests to their parametric "cousins" (in which it was initially argued that nonparametrics were much less powerful -- which is why we haven't traditionally used them as much as parametrics -- and later finding that even fairly minor deviations from assumptions lower the power of parametric tests enough to make nonparametrics highly competitive -- which is why there is now renewed interest in them).
Regards,
--
Christopher D. Green
Department of Psychology
York University
Toronto, ON M3J 1P3
Canada
416-736-5115 ex. 66164
[EMAIL PROTECTED]
http://www.yorku.ca/christo
=============================
Marc Carter wrote:
Seconded.
I'd be interested in hearing about this, too. It seems to me that the computation of power has to make assumptions about the shape of the distribution of the dependent variable (power is essentially a measure of area of the distribution of the variable -- under the alternative hypothesis -- above the criterion), and so if we cannot make assumptions about the character of that distribution (that's why they're called "distribution-free stats"), I'm at a loss to figure how we'd compute its area.
I'm wondering if there's some way to bootstrap a distribution based on the data, generate a function to describe it, and then get about integrating it.
But, as often happens, I could be wrong and would really like to know.
m
-------
"Mauchly's Test of Sphericity:
Tests the null hypothesis that the error covariance matrix of the
orthonormalized transformed dependent variables is proportional
to an identity matrix."
---
SPSS
---
To make changes to your subscription go to:
http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
---
To make changes to your subscription go to:
http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
---
To make changes to your subscription go to:
http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
--- To make changes to your subscription go to: http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
---
To make changes to your subscription go to:
http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
|
