separately posted to sci.stat.consult, sci.stat.edu
On Mon, 25 Dec 2000 17:51:14 +0800, Wen-Feng Hsiao
<[EMAIL PROTECTED]> wrote:
> Dear all,
>
> Paired t-test helps us to exam whether the paired samples (or the same
> samples) respond differently between two treatments. The null hypothesis
> is H0: mu1=mu2 or mu1-mu2=0. Could this be extended to test a null
> hypothesis with H0: mu1-mu2=C, where C is a constant, but unknown. How?
Your regular, paired t-test lets you draw the Confidence interval for
the difference. Does it include 0? Does it include C? - not much of
an extension.
> My intention is to show that the treatment effect only affects the shift,
> but not the shape of the distribution as the following ASCII-graph.
I hope I am not reading the wrong thing into the question here,
but I was once baffled by a similar problem.
I will re-state the question, in the way that it has confronted me.
I have never seen a good answer - one that I would
convince everyone else.
Here is my own numeric version for Pre-Post scores,
instead of an ASCII picture.
Model A: scores (1,2,3,4,5) are *shifted* by 3 points each, to
(4,5,6,7,8).
Model B: scores (1,2,3,4,5) are each expanded 3-fold, to
(3,6,9,12,15).
Descriptively: Model B is "wider" at Post than at Pre; the variance
of change scores is correlated with the scores.
Unfortunately, that conclusion, or description, is not scale-free.
Once you take the logarithm for data in Model B, Model B would be
"shifted", not expanded.
- for small sets of data, you can't tell anything apart.
- for larger sets, I think you can compare the number of scores
at the low end. It does depend on the mechanism that you assume is
generating the numbers. However, I have seen data where (I thought)
the bottom end showed "shift" because of how thin one density was.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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