Dear Eric,
> Regarding Cindy's question, isn't there an issue of the ability to
> falsify? That is, even though she could include a score X
> pharmacological challenge interaction in the model, what would be the
> confidence in a negative result? It seems from the wording of her
> question that sensitivity might be her primary concern. If so, the
> answer would depend upon the effect size of interest as well as the
> sample size and covariance of this interaction term with the group by
> pharmacological challenge interaction term.
I'm sure your absolutely right. Any analysis with only 6 subjects will
have low power. If the null hypothesis of no score x challenge
interaction can be rejected then that would be very nice. A null
result however is quite likely and in this case no inference can be
made.
In relation to 'the ability to falsify'. One can never falsify the
alternate hypothesis. A null result simply means that one failed to
detect an effect. Put simply one can never accept the null
hypothesis. People generally try to reframe questions about 'no
effect' in terms of interactions, so that the problem is converted to
rejecting the null hypothesis of no difference where you would expect
to see one.
Very best wishes - Karl
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