----- Original Message -----
From:
I wrote:
> > (4) In order to avoid circular logic, we *cannot* assume what we
want to
> > prove, in order to compute the probability. We can however assume it for
a
> > contradiction. Therefore...
and Michael Granaas responded
> This (point 4) is certainly what we have been lead to believe, but I
> question the assumption. Do we not in fact teach that we are to act as if
> the null is true until we can demonstrate otherwise?
I certainly don't. We *compute* as if the null was true, whether we
believe it or not; then we either conclude that (null + data) is implausible
or that the data are consistent with the null.
> Isn't that what we do in our experiments all the time? We assume that our
> experimental manipulation has no effect, which is plausibly true at least
> for some time, and then we try to disprove that estimate of the effect.
> Failing to do so we act as if the effect were absent (or so small as to be
> absent for all practical purposes).
We have no right to do the latter unless we ahve actually estimated
effect
and it *is* that small.
And again:
> > (7) Back at the beginning we wanted a yes-or-no answer. Henced fixed
> > alpha testing and the pretence that we "accept" null hypotheses.
>
> If the null is plausibly true we need no pretense. We accept the null as
> true until something better comes along. I personally have accepted the
> notion that psi powers do not exist despite the fact that all I have is a
> string of failures to reject the null as evidence.
Spoken like a Bayesian, sir! But if you talk the talk you should also
walk the walk. Hypothesis testing does not give you any way to formally
introduce the idea that a null is "plausibly true". Bayesian inference does.
> > OK, it's a horrible kludge at best, and an evil ritual at worst; but
> > *if* you start with those assumptions & goals, there's what comes out.
>
> Yes. Since I refuse to start with assumption that the null must be false
> to be useful I end up in a somewhat different place.
Starting from there, you *should* end up in Bayesian inference, or at
least likelihood-based inference. If you want to be able to conclude that
the null is plausibly true, you must not start out by assuming its truth
even
as a working assumption. You can assume nothing, and compare likelihoods;
or
you can assume some _probability_ for the null and see what the data do
to that assumption, via Bayes' theorem. But if you assume truth, you can
get
only a contradiction (null + data => improbable) or a tautology
(null + data => null) that does not function as a proof.
-Robert Dawson
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