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List:       sas-l
Subject:    Re: Two Sample t-test (Both samples have 1st order
From:       "David L. Cassell" <cassell.david () EPAMAIL ! EPA ! GOV>
Date:       2003-10-31 18:19:26
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Steven Hill <hills@sfwmd.gov> replied to me personally (instead of
replying to SAS-L):
> I hear and understand what you are saying.  My overall goal with this
data
> is to test if there is a significant difference between the means at
the
> alpha=0.05 level.
> So are you saying that this cannot be done correctly?

If you really have serial correlation, then, depending on the underlying
model, you may not even have a fixed mean for one series (or for both
series).
And, clearly, if your mean varies over time, you can't treat all your
data
as having a single mean value.  So the basic hypothesis needs to be
re-worked.

So I really think that you need to evaluate your data first:
Do you have a fixed mean, or do you have a trend?
Do you have correlation between your series?
Do you have first-order correlation in one or both series?
Is your correlation structure easily modeled using an ARIMA model?
Does the cross-correlation between series actually drive the apparent
    corelation within series?
If the two series are strongly correlated, do the differences (of one
    variable minus the other) behave better?
Can you model the behavior of one or both series?

Then you need to look at your hypotheses in light of the results:
If you have a moving mean, how would you re-state your basic hypothesis?
If you have a fixed mean, and the two series are strongly correlated,
how would you re-state your basic hypothesis?
If the two series are strongly correlated, would it make more sense to
look at the differences and assess whether the differences are
significantly
larger than zero?

HTH,
David
--
David Cassell, CSC
Cassell.David@epa.gov
Senior computing specialist
mathematical statistician

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