I want to show that the mean age of test person does NOT differ
significantly in two groups, for example men and women.

The t-Test can show that they are NOT equal but which test shows that
they ARE equal?

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Clarification of Question by jennybo-ga on 09 Oct 2004 09:51 PDT

I want to analyse the influence of gender on various dependant
variables (using regression). For this I have two groups of test
person, men and women. Since age also has a large influence on the
dependend variables I need to show that the two groups dont't differ
significantly in age.

Can I use the t-Test and argue like this: The null hypothesis that the
two means of age are equal can not be (does not have to be?) rejected
because the level of significance is greater than 0,05 (0,30 for
example).

Or how else can I show that the difference in the mean age of the two
groups does not influence the dependant variables?

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Request for Question Clarification by mathtalk-ga on 09 Oct 2004 22:18 PDT

One approach would be to show by regression that age differences do
not account for a large fraction of the variation between the two
groups.  In other words, treat age and gender as two independent
variables and analyze variance in the dependent outcome in terms of
these for the entire sample.

regards, mathtalk-ga

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Clarification of Question by jennybo-ga on 13 Oct 2004 14:38 PDT

Thank you for your answers! That helped. I tested the variables in a regression.

I'm not so familiar with Google Answers. What do I need to do in order
to pay for your answer?

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Request for Question Clarification by mathtalk-ga on 13 Oct 2004 14:45 PDT

Hi, jennybo-ga:

I just need to post an Answer in the answer box!  Let me dress up what
I said a bit and that's what I'll do.

regards, mathtalk-ga

Hi, jennybo-ga:

In your sampling you have two genders and a variety of ages in each
group.  One approach to analyzing such data when the outcome may
depend both on the age and gender is through regression, which you
have tried.

If we could go back in time and redesign your "experiment", an
alternative approach might more closely meet the intuitive idea of
eliminating age as a factor from the analysis.  Such an approach is
called matched or paired observations.  In other words, prior to
measuring the outcome or dependent variable, one pairs up individuals
from the two groups so that their ages are equal (or nearly so).  Then
the analysis of the outcomes can be done using the gender variable
within each pair.

The "cost" of such a paired observation study is naturally a bit
higher than one which accepts observations of unmatched samples.  It
commits one to equal sample sizes of men and women, for example, and
carries a greater risk of "losing" data over the course of a study
when one or the other of a pair must drop out.

So, for the sake of thinking about "next time", here are a couple of
sites that explain some of the theory and the procedures involved.

[Analysis of paired observations - NIST]
http://www.itl.nist.gov/div898/handbook/prc/section3/prc311.htm

[Testing paired observations online]
http://home.clara.net/sisa/pairwhlp.htm

regards, mathtalk-ga

Very helpful!

Hi, jennybo-ga:

In essence there is no separate test which "shows that they ARE equal".

Let's back up a step and make sure we're talking about the same issue.
 There are two populations, and for each we have a random sample of
ages (e.g. of men and of women as you suggest).

If we have the _entire_ population for both groups, then of course we
can calculate the two means.  That would accordingly tell whether the
two means are equal or not.

With only a sample, however, the exact population mean is not known. 
Under these conditions the best we can hope for is a technique like
Student's t-test that says whether the sample results are reasonably
likely _if_ the population means were equal.

[Here we come to a subtlety that you may or may not intend to
introduce.  The usual "null hypothesis" would be that the two samples
are drawn from the same underlying population, or equivalently that
the two populations have the same distribution.  In that case both the
means and the variances (and other statistics) for the two populations
will agree.  So it's conceivable that you are asking for tests that
check equality of means under a "broader" null hypothesis, in which
means might be equal but variances (or equiv. standard deviations) are
unequal.]

Student's t-test relies on a normal approximation to the distribution
of sample means.  For this approximation to be valid requires a
modestly large sample size in relation to the population variance. 
There are other "robust" statistics which are useful in situations
where a normal approximation is suspect.  For example, a normal
distribution is continuous but "age" is normally recorded in whole
numbers, which produces a discrete distribution for means of a fixed
sample size.  [As sample size grows the distinction becomes less
significant.]

regards, mathtalk-ga