Re: Hypothesis testing on a NON normal distribution

From: Glen (glenbarnett_at_geocities.com)
Date: 08/24/04 

Date: 23 Aug 2004 18:23:17 -0700

"Anonymous" <anon@inter.net> wrote in message news:<lYqdnSDAGs8Y-rTcRVn-pQ@giganews.com>...
> I want to do hypothesis testing on a distrubition that IS known, but is NOT
> the normal distribution (triangular for example).
>
> I know f (the frequency density function), F (the cumulative distribution
> function), the theoretical mean, st.dev., etc.
>
> What I don't know I how to do the hypothesis testing. I know the equations
> for normal, can anyhow give me analoguous equation for other distributions
> based on their parameters and alpha/beta (type I/II errors)? Specifically:
> "are the samples in group A significantly different from those in group B"
> (testing for differences on mean and st.dev).

Are you interested in /any/ differences in distribution, or only differences
in mean and standard deviation?

Are you interested in testing for differences in both mean and standard
deviation at the same time, or just one or the other at a given time?

Does the distribution have specific location and scale parameters
(perhaps its a location-scale family of distributions), or is it
more complicated?

Essentially, the question comes down to
"can you construct a likelihood ratio test?"

Failing that there are some other approaches that might be taken.

If you are interested in testing for both location and scale
differences at the same time, besides parametric tests, there
are also some nonparametric tests available.

That said, the t-test for location difference isn't terribly sensitive
to deviations from normality (it does have some sensitivity to strong
skewness).

Glen

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