> Hi,

is a common argument in simulation experiments, that because you can do an

>

> I'm not sure i agree with the idea that a test can be too powerful. This

infinite number of replicate simulations, somehow the differences

detected are not real. In fact, the differences are real. They may not

be biologically (or geologically or whatever field you are in)

significant, but they are still real. That is why it is better to decide

first on the magnitude of difference that you consider significant.

The null hypothesis is always false although it might be false by a very

small quantity, that is the trivial fact that the very large sample size

illustrates in the common test of significance. The conclusion to be drawn

from this is not that we must set in advance the amount of difference that

we would find significant (a rather restrictive strategy which will be

violated very often because it is nonsensical), but rather that the only

sensible strategy is to compare hypotheses one against another. This can

be done on an evidential basis by evaluating the likelihood ratio, the

likelihood of the data under one hypothesis divided by the likelihood of

the data under another hypothesis. By constructing the whole likelihood

function (in the case of a single parameter) any pair of hypotheses can be

tested for the value of the likelihood ratio.

> Now, in the case of deviation from normality, I suppose you wouldn't

have much intuition about what is significant, but the relevant question

is what is the effect of small deviations from normality on your test or

conclusions of your analysis?

Perhaps a better question is what the data say about a given hypothesis

for the mean versus another value for the mean assuming the normal

distribution is true? If the variance is unknown there is a simple

solution only for the normal and a few other cases, by orthogonalization,

and then the two parameters can be assessed separately. For comparing two

different models, say normal versus lognormal, a likelihood based

approach, the Akaike Information Criterion, is available although i am not

sure that Akaike's approach is fully in agreement with the likelihood

principle.

Ruben

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