Re: normality of residuals
- From: glenbarnett@xxxxxxxxxxxxx
- Date: 14 Jul 2005 18:28:18 -0700
Don't do formal hypothesis tests, because they answer the wrong
question -
the question isn't "Can I tell my data are non-normal?"
it's "How badly is my non-normality going to affect my inference?"
And that depends on a whole lot of things, but doesn't depend much at
all on sample size (which impacts the first question in a big way).
It suggest, for example, looking at measures of the degree of
non-normality you have (measuring the aspects of the distribution that
impact the things you're interested in).
If you're interested in prediction intervals, you depend heavily on
normality. If you're interested in hypothesis tests or confidence
intervals you depend a little less heavily on normality. If you're
interested in just estimating the coefficients themselves, you're not
that dependent on normality at all (if things are badly non-normal your
estimates will be inefficient, but that may not be a problem with
really large sample sizes).
If the residuals aren't badly skewed or heavy-tailed and you just want
to estimate coefficients, normality isn't a prime consideration. It's
more important to make sure the model for the mean is of the right
form. Then worry about things like equality of variance. Then worry
about normality.
If, however, you want prediction intervals (in most applications I deal
with, that's of primary interest), then you depend heavily on the
distributional assumption.
As far as checking normality, diagnostics such as P-P plots or Q-Q
plots are fine. If you have more specific ideas about what you need to
check for (in your case I'd expect skewness), you may want to check
some other diagnostics as well, but in general a Q-Q plot
(specifically, a normal scores plot in this case) is a good general
purpose check on the assumption. It tells you something about where and
how badly you deviate from normality.
To get used to reading such plots, it helps to generate a number of
sets of normal data and fit regressions to see what normal residuals
can look like. Then generate some non-normal data (skewed, heavy
tailed, data with the odd outlier, light tailed, whatever you like) and
see what their plots look like.
Glen
.
- References:
- normality of residuals
- From: thierry
- normality of residuals
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