Date: Dec 2, 2012 1:27 AM 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 30, 8:37 pm, Ray Koopman <koop...@sfu.ca> wrote:

> 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.

Nevertheless, plots of SE*sqrt[n] against the width of the length

interval are close enough to linear to make me wonder if we should

revert to equal-width intervals. (The current equal-ratio intervals

were designed for logging.)