Kristen --
To me, this appears to be an equivalence testing problem, similar to what I
asked about a few days ago. Stata has program -pkequiv- for performing an
equivalence test for paired data derived from a crossover design but it does
not have a module for a simple two-independent-samples design. I have been
investigating how to determine the "classic confidence interval for
bioequivalence" for non-crossover designs and it seems straightforward using
elementary features of Stata. I suspect that the TOST (two one-sided
t-tests) procedure can also be carried out using elementary features, but I
have not confirmed that yet.
The classic and TOST procedures use a null hypothesis that your two
concentrations differ more than a fixed amount (equal StDev in your case)
vs. an alternative hypothesis that the concentrations are equal. You hope
to reject the null so you can declare equality. From my initial reading,
the classic analysis appears to be equivalent to confirming that the 90% CI
about the difference in concentrations (Diff) falls completely in the
interval
Diff - StDev -------- Diff + StDev
where StDev is the fixed amount the two concentrations are allowed to
differ.
If so, then all you need to do is generate an appropriate 90% CI and confirm
it does (or does not) fall fully in the above interval. -ttest- can be used
to calculate the CI and it will easily handle the unequal n situation you
have.
If anyone will confirm (or deny) that this is an appropriate approach to
performing the "classic confidence interval for bioequivalence" for
independent designs, I would appreciate it.
Tom
----- Original Message -----
From: "Wandland, Kristen" <[email protected]>
To: <[email protected]>
Cc: "Perry, Elizabeth" <[email protected]>
Sent: Friday, January 16, 2004 9:10 AM
Subject: Re: st: Re: specifying difference in H0 of ttest
> At 11:28 AM 1/15/2004 -0500, Wandland, Kristen wrote:
> Thank you all for the information so far. I have yet to digest it
> all!
>
> I think I should help with a couple of clarifications: we are
> looking at
> potentially uneven sampling groups (n1 = 10, n2 = 15) and we do have
> unequal
> variances.
>
> The ultimate task at hand is to determine if the concentrations (of
> a
> constituent) from one area are consistent with the concentrations
> from the
> other area. EPA has requested a ttest with diff = StDev.
>
> In that case my clunky solution from before may not be so bad after all
> (although somebody will no doubt suggest yet another better way to do
it!).
> I'm not sure what StDev you are referring to (the SD for Y with both
groups
> pooled together?) but anyway lets assume you have determined it is 10; and
> lets further assume the hypothesis is one tailed in that you expect group
1
> to be the group that scores higher. Then
>
> gen score2 = score
> replace score2 = score2-10 if group==1
> ttest score2, by(group) unequal
>
> You could modify this along the lines of what Scott suggested to use the
> saved results from summarize. Does this sound like what you wanted?
> -------------------------------------------
> Richard Williams, Associate Professor
>
>
> This is potentially exactly what I wanted. I need to try it all out, but
in
> syntax it looks like it'll work.
> Thank you ALL for input!
>
> Kristen Durocher Wandland
> ENSR
> 7041 Old Wake Forest Road
> Raleigh, NC 27616
> 919-872-6600
>
>
>
>
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