Date:         Thu, 28 May 2009 15:24:09 -0400
Reply-To:     Peter Flom <peterflomconsulting@mindspring.com>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Peter Flom <peterflomconsulting@MINDSPRING.COM>
Subject:      Are tests of normality useful for model checking?
Content-Type: text/plain; charset=UTF-8

Thinking some more about tests of normality for model fit.

Are these useful?

Let's say some model assumes the errors are normally distributed.  Do these models
fail when the residuals are SIGNIFICANTLY non-normal?  Nope.  That's never the case, AFAIK.
They fail (or fail to a greater degree) when the residuals are IMPORTANTLY non-normal, and
they probably fail worse for certain kinds of non-normality than for other types.

So, rather than standard practice being, e.g.:
1) Run PROC GLM
2) Test the residuals for normality
3) If the test is passed (p > .05) proceed, if the test fails, do something else

Shouldn't it be
1) Run PROC GLM
2) Plot the residuals in a QQ plot
3) Check if any are far from the line and examine those closely
4) If there are deviations, do something else and compare the results?
5) If the results are similar in PROC GLM and something else, use PROC GLM, for simplicity
   If the results are not similar, use the alternative, or look further

How similar?  Similar enough!

If you (or the people you are working with) can't tell if results are substantively similar,
how will they interpret any results of any analysis?


Peter



Peter L. Flom, PhD
Statistical Consultant
www DOT peterflomconsulting DOT com