Re: test for equal

yaobinmail@xxxxxxxxx wrote in news:1141228207.847910.12600
@j33g2000cwa.googlegroups.com:

I have 2 groups of samples and I example some gene expressions in each
sample. The goal is to find genes that have different expression levels
between and genes that have same expression levels between group. For
the first one I used t-test and p<0.05. I think for these genes that
have p >0.05 can't be called equal because the p value control the
positive not the false negative. Type II error seems right but it
requires expected difference that we don't know. Can I use the
difference from the data or the difference has to be known priori to
the test. Is there any other way to test equal (H0: unequal. H1: equal)
only use existing data?

You have reversed the conventional order. Ho is usually the null. That is
only a convention, so in a sense you might already be already testing
H1:equal vs H2:unequal depending on the actual mechanics you are using.

The paired hypotheses you offer would imply a test that will not
distinguish mean>mu from mean<mu. (Am I correct in thinking that you do
not even know to high accuracy what the mu (pre-established mean) should
be in a "normal" sample?) In all likelihood your formulation does not fit
your scientific position of no prior knowledge regarding whether a
particular group will have gene expression repressed or over-expressed. I
cannot quite believe that if you found a gene that was materially and
predictably lower in the diseased goup that you would throw that
knowledge away. You would probably patent the product that could be
created. It would be more in keeping with what appears to be the level of
knowledge of the science (the a priori statistical state) to do your
statistical testing in a manner that does distinguish between repression
and derepression.

If for some reason, you really only would be interested in a gene that
were over-expressed, then a one-tailed test would be used. It would test
mean>mu vs mean<= mu.

If you want to increase the power of the two sided t-test, without
throwing away useful knowledge about the signs of the differences, you
can increase the alpha from 0.05 to 0.10 (or even to 0.20). There is
nothing sacred about p<0.05. The decision regarding what the "p-value" is
would express the level of your belief that you were in a search mode and
would be subjecting any "finds" to further testing and scrutiny. That
does bring oup the thorny subject of sequential testing, so maybe you
should just quadruple your sample sizes, instead. There, wasn't that
easy?

If you really want to consider the hypothesis you propose, there is a
biostatistical literature on tests of equivalence. The hypothesis could
be formulated Ho: (observed mean minus prior-mean) < 95% or 110% of
prior-mean vs Ha. This is appopropriate in pharmacologic investigations
where a new drug is being tested against a drug of established value. In
that setting the goal is to reject any candidate drugs that are inferior
to the current drug. If it is equvalent or better, it is a keeper. For
the reasons I have expressed, I do not think you should expend the
effort, since I do not think it is appropriate to the sort of science you
are (probably) doing.

--
David Winsemius, MD
.