Date: Nov 30, 2012 11:37 PM
Author: Ray Koopman
Subject: Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions<br> regarding them ...)

On Nov 29, 8:29 am, djh <halitsk...@att.net> wrote:
> Here are the SE?s for average slopes for a1_N_1_S and a1_N_1_C:
>
> a1_N_1_S:
>
> Len
> ID obsN Avg Slope Avg slope SE
>
> 1 215 -4.805470268 0.950050755
> 2 314 -2.595530566 0.959429879
> 3 311 -2.291065716 1.024763870
> 4 210 -2.389119127 1.471966277
> 5 256 -1.215695376 1.398629841
> 6 246 -0.262323729 1.643926445
> 7 226 1.363522805 1.611512322
> 8 278 -0.560630170 1.620693559
> 9 246 2.374377463 1.847997565
> 10 211 -0.816451823 2.632764400
> 11 194 -0.499208768 2.855882984
> 12 234 1.968865343 2.864247061
>
> a1_N_1_C:
>
> Len
> ID obsN Avg Slope Avg slope SE
> 1 166 -2.225882168 0.813316857
> 2 265 -2.315512399 0.693531939
> 3 258 -0.769858117 0.939333935
> 4 188 -1.697049757 1.291121211
> 5 243 -2.069842267 1.245969677
> 6 228 -4.427566827 1.508641800
> 7 219 -0.941379623 1.493402326
> 8 263 -2.069096413 1.534849449
> 9 233 -1.620229799 1.518979934
> 10 199 -3.764328472 2.294575586
> 11 185 -7.882327621 2.694025880
> 12 232 -11.82556530 3.055385684
>
> You?ll see that:
>
> a) for a1_N_1_S, going to the bounds implied by the SE will not change
> the sign of the average slope only up to length interval 4 ? after
> that the SE generally will;
>
> b) for a1_N_1_C, the SE will only change the sign of the average slope
> in two cases out of the 12: length intervals 3 and 7;
>
> c) in both cases, SE increases considerably with length but ?much more
> so? (?) for a1_N_1_C than for a1_N_1_S.
>
> If it?s legit to draw conclusions from comparative behavior of SE?s in
> contrasting sets of results like these, then interesting scientific
> interpretations can be made of the above SE behaviors. But I?ve
> learned not to jump the gun by making such interpretations based on
> illegitimate interpretations of statistical behaviors. So, guidance
> please, when you have a chance.
>
> Also, regarding point (c) above, if it?s legitimate in general to look
> at SE behavior in such results sets, is there a legitimate way to show
> that the SE?s for a1_N_1_C really do increase significantly MORE with
> increasing length interval than SE?s for a1_N_1_S? Or not? Again,
> guidance please.
>
> And thanks again as always for your continued consideration of these
> matters.


SE's of slopes depend on n, the distribution of the predictors,
and the standard error of prediction, only the last of which is a
"structural parameter", something that is intrinsic to the phenomenon
being studied. The other two are "design parameters" that are to some
extent arbitrary and therefore not proper objects of hypotheses.

It is legitimate to compare standard errors of prediction, but it's
harder than comparing means or slopes. I would steer clear unless you
have nothing else to keep you busy.