Re: t-test?

On Oct 22, 4:31 am, diodoo <sunj...@xxxxxxxxx> wrote:
Hello everyone!

Suppose I have a measurement of a variable for two different groups (of different sizes), coming from non-normal distributions, and I want to day something about their means.

I cannot use an unpaired student t-test because of the non-normalities.

However, for each of the groups I can calulate, say, the 95% conf. interval of their means using t distributions. Then, if the conf. intervals for the two means overlap, can I say that the means are not significantly different (at 95% conf. level)? If so, wouldn't this be equivalent to performing an unpaired student t-test?

(I don't want to use the Mann-Whitney U test, because that tests the medians...)

Thanks!
Diodoo

Where to start?

1. If you're working with real data, the distributions are never
normal. So the t-test (with real data) is an approximate test, not an
exact test. But, it is quite robust to skewness, provided the two
distributions are similarly shaped. Here is a quote from Dave
Howell's book "Statistical Methods for Psychology" (1997 edition, p.
321):

"In general, if the populations can be assumed to be symmetric, or at
least similar in shape (e.g., all negatively skewed), and if the
largest [sample] variance is no more than four times the smallest, the
analysis of variance is most likely to be valid. It is important to
note, however, that heterogeneity of variance and unequal sample sizes
do not mix. If you have reason to anticipate unequal variances, make
every effort to keep your sample sizes as equal as possible."

2. If the data are such that the t-test is not valid (i.e., the
approximation is not good enough), then the 95% confidence intervals
will not be any better.

3. Overlap of the 95% CI's must not be used as a test on the
difference between the means. There can be substantial overlap when
the difference between the means is significant. You would need to
look at the 95% CI on the *difference* between the two means. See the
following:

www.angelfire.com/wv/bwhomedir/notes/thorpe_ci_examples.pdf
http://www.cmaj.ca/cgi/content/full/166/1/65

4. Re your statement about the Mann-Whitney U test comparing medians,
see the Common Questions section of the following:

http://www.bmj.com/statsbk/10.dtl

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
"When all else fails, RTFM."

.

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