On Sep 5, 6:10 am, djh <halitsk...@att.net> wrote: > You wrote: >> We compare sample statistics and functions thereof because we want >> to say something about the corresponding parameters. The bigger >> the N's, the closer the sample statistics are likely to be to the >> parameters, and the clearer the inferences will be. Conversely, the >> smaller the N's, the farther the sample statistics are likely to be >> from the parameters, and the more difficult it will be to draw firm >> conclusions. In short, we ask questions about parameters, and N's >> have no part in that, but the clarity of the answers we get is >> inescapably determined by the N's. > > So since I'm both naive and ignorant, the question that occurs to me > is the following. > > Suppose we take your original custom heteroscedastic t-test "T" and > execute it on 12 pairs of corresponding non-random and random slopes > and SE's: > > Non-Random Random > S1 SE1 S'1 SE'1 > > ... > > S12 SE12 S'1 SE'12 > > where: > > i) S1...S12 (and SE1...SE12) are derived from data for the 12 length > intervals in the non-random data frame (a1,63,S,uH,A) > > ii) S'1...S'12 (and SE'1...SE'12) are derived data for the 12 length > intervals in the random data frame (a1,R63,S,uH,A) > > Given the fact that Ni and N'i (1<=i<=12) will differ to a greater or > lesser degree (because we haven't bootstrapped), is there some > generally accepted function of ((N1,N'1),...,(N12,N'12)) that will > yield a degree of confidence associated with the t (or p) returned by > "T" ? > > And if not, can you construct one that you personally would accept > (i.e. would be willing to fight over with referees?)
I'm not sure what you mean by "degree of confidence associated with t (or p)", but if it's what I suspect then the answer is No. That is, if you're thinking about something like the "master significance tables" of previous posts then there is no way to adjust the p's to what they would have been if the N's had been different from what they actually are, or to adjust the threshholds for declaring significance in such a way as to counteract differences among the N's.