[EMAIL PROTECTED] wrote:
> Paul and Gus,
>
> The point of finding a subsample is to get rid of the normal distribution
> and replace it with a uniform sample that allows the concurrence of similar
> extremes of both causes. If we start with a normal distribution and want a
> uniform, then a random subsample will NOT do. All that would do is give us
> back a picture of the same original normal sample, but with smaller sample
> size.
>
> I can not seem to communicate that normal distributions are not better than
> others, just because we often get normal distributions from snap shots.
> Just going out and taking a snap shot of some phenomenon is likely to leave
> us with the extremes of the causes under sampled... a normal distribution.
> I know this statement challenges a very large number of studies in many
> disciplines. But I was not the first to so challenge. Nunnally called
> normally sampled causes "dead data." Only the effects should be sampled as
> normal or triangular.
My ignorance shows, since I have no clue as to who Nunnally was.
At any rate, I think he is quite wrong. My problem with his position
is that it _presupposes_ that I know what are the causes and the
effects. If I then want to use CR to classify my variables, that is
circular logic.
Here are two data sets for you:
Sample 1 Sample 2
x1 x2 x3 x1 x2 x3
-0.1080 0.3953 0.5033 -0.4397 0.2960 -0.1437
-0.0397 -0.4221 -0.3824 0.1654 -0.0392 0.1262
0.1731 -0.3578 -0.5309 -0.1806 -0.3556 -0.5362
-0.1922 -0.3609 -0.1687 0.3486 -0.2583 0.0903
-0.4954 0.0686 0.5640 -0.3397 -0.2943 -0.6340
0.1204 0.2726 0.1522 0.2225 0.2985 0.5210
0.2326 -0.1835 -0.4161 0.4383 0.1177 0.5560
0.0382 -0.1677 -0.2059 0.4894 -0.1643 0.3251
0.1101 -0.2875 -0.3976 0.2245 0.3840 0.6085
0.2314 -0.0712 -0.3026 -0.1449 -0.1220 -0.2669
0.1834 -0.0154 -0.1988 0.3106 -0.3532 -0.0426
-0.3144 -0.3424 -0.0280 -0.0671 -0.2752 -0.3423
-0.1609 -0.1717 -0.0108 -0.0526 0.1395 0.0869
-0.3071 -0.0672 0.2399 -0.0737 -0.4318 -0.5055
0.3023 0.3298 0.0275 -0.4424 -0.1317 -0.5741
-0.3086 -0.1721 0.1365 -0.2790 -0.3178 -0.5968
-0.0301 0.4549 0.4850 0.1514 0.2256 0.3770
-0.4170 0.4049 0.8219 0.3591 -0.1085 0.2506
0.3822 0.4298 0.0476 0.0932 -0.3287 -0.2355
0.4678 -0.3920 -0.8598 -0.2843 0.3962 0.1119
-0.3454 0.4602 0.8056 -0.1186 0.0616 -0.0570
-0.1997 -0.4107 -0.2110 0.3543 0.4832 0.8375
-0.0753 -0.2161 -0.1408 -0.0579 -0.3364 -0.3943
0.4514 0.3021 -0.1493 0.0820 0.4140 0.4960
-0.4914 0.1282 0.6196 0.0238 0.2010 0.2248
-0.3188 -0.2597 0.0591 -0.4660 -0.0083 -0.4743
0.0954 -0.4192 -0.5146 0.3160 0.1450 0.4610
0.3109 -0.1859 -0.4968 0.2707 -0.3065 -0.0358
0.1177 0.0425 -0.0752 -0.1334 -0.4000 -0.5334
0.0988 0.0866 -0.0122 0.3131 0.0778 0.3909
0.2042 -0.3173 -0.5215 0.1473 -0.3525 -0.2052
0.4936 0.0075 -0.4861 0.1552 0.3760 0.5312
0.3995 0.1239 -0.2756 -0.4542 0.3861 -0.0681
-0.2928 0.1044 0.3972 -0.1404 0.3967 0.2563
-0.2079 -0.4417 -0.2338 0.0219 -0.1143 -0.0924
-0.2872 0.2315 0.5187 -0.2758 0.0582 -0.2176
0.0952 0.2241 0.1289 0.1723 0.1686 0.3409
0.0612 0.4615 0.4003 0.0937 -0.4729 -0.3792
0.0994 -0.3605 -0.4599 -0.0574 0.0202 -0.0372
-0.2700 -0.0366 0.2334 0.0330 0.1393 0.1723
0.2352 -0.2092 -0.4444 -0.1287 0.4526 0.3239
-0.3092 0.3306 0.6398 0.4807 -0.4881 -0.0074
-0.3007 0.2191 0.5198 0.1418 0.0555 0.1973
-0.0645 -0.1181 -0.0536 -0.1412 0.2659 0.1247
0.1709 -0.1709 -0.3418 0.0594 -0.2961 -0.2367
0.4761 0.4055 -0.0706 -0.4084 -0.3958 -0.8042
-0.4904 0.2683 0.7587 -0.3724 0.4771 0.1047
-0.2681 0.0731 0.3412 -0.0559 -0.0793 -0.1352
-0.0226 0.2264 0.2490 -0.0836 0.2387 0.1551
0.1847 0.1867 0.0020 0.2396 0.0202 0.2598
0.2076 0.2120 0.0044 -0.3015 0.0792 -0.2223
0.2451 0.4303 0.1852 -0.3462 0.3331 -0.0131
-0.0490 -0.0084 0.0406 -0.1550 -0.0568 -0.2118
-0.0365 -0.3069 -0.2704 -0.3262 -0.3329 -0.6591
0.2611 0.3574 0.0963 0.4767 0.2800 0.7567
-0.0611 0.1078 0.1689 -0.1874 -0.2461 -0.4335
-0.1591 -0.0597 0.0994 0.0916 0.0904 0.1820
0.3689 -0.2308 -0.5997 -0.4325 0.0419 -0.3906
0.2228 -0.4240 -0.6468 -0.4178 -0.4326 -0.8504
0.4775 -0.2383 -0.7158 0.4032 -0.2920 0.1112
0.3783 -0.0090 -0.3873 0.3121 0.2828 0.5949
-0.0566 0.0260 0.0826 0.3388 0.3410 0.6798
0.4026 0.1592 -0.2434 0.0499 0.3937 0.4436
-0.1845 0.1619 0.3464 -0.2070 -0.2163 -0.4233
-0.2490 -0.1894 0.0596 0.1267 0.4613 0.5880
0.3668 -0.3443 -0.7111 -0.0371 0.4682 0.4311
-0.4651 -0.0808 0.3843 -0.0616 0.3536 0.2920
0.3750 0.0377 -0.3373 0.2678 -0.0612 0.2066
-0.1645 -0.2539 -0.0894 0.0980 -0.0522 0.0458
0.4041 -0.1345 -0.5386 -0.2904 -0.0675 -0.3579
0.0645 -0.2520 -0.3165 0.1373 -0.1961 -0.0588
0.0621 0.3327 0.2706 -0.1248 0.1215 -0.0033
-0.1591 0.4404 0.5995 -0.3287 -0.4614 -0.7901
0.1182 -0.4835 -0.6017 -0.3457 0.2191 -0.1266
-0.2415 -0.2480 -0.0065 0.2812 0.4961 0.7773
-0.3003 -0.4429 -0.1426 0.1968 -0.2689 -0.0721
0.1662 0.3290 0.1628 -0.4027 0.4364 0.0337
-0.2538 0.4813 0.7351 0.4085 0.3003 0.7088
0.2485 0.1853 -0.0632 -0.3424 -0.1506 -0.4930
-0.2859 -0.3326 -0.0467 -0.2163 0.4987 0.2824
-0.1710 0.0792 0.2502 -0.2549 0.2514 -0.0035
0.0548 -0.0992 -0.1540 -0.0244 -0.1422 -0.1666
0.0410 0.1996 0.1586 0.4855 0.4630 0.9485
0.3219 0.2388 -0.0831 0.3642 -0.0608 0.3034
0.4776 0.2809 -0.1967 -0.3695 -0.0575 -0.4270
-0.0407 0.3851 0.4258 0.2506 -0.2512 -0.0006
-0.3385 0.0563 0.3948 -0.2974 -0.4193 -0.7167
0.3362 -0.4555 -0.7917 -0.4036 -0.2230 -0.6266
-0.4863 -0.3058 0.1805 0.2822 -0.1218 0.1604
-0.3244 0.1590 0.4834 -0.2181 0.1220 -0.0961
-0.2982 0.3868 0.6850 -0.4685 0.1107 -0.3578
-0.4723 -0.1808 0.2915 0.4669 0.0894 0.5563
-0.4189 -0.2992 0.1197 -0.3594 0.1894 -0.1700
0.1484 0.4720 0.3236 0.4702 -0.3301 0.1401
0.4847 -0.4153 -0.9000 0.4001 -0.0267 0.3734
-0.4401 0.3119 0.7520 0.2147 -0.4939 -0.2792
0.2471 0.0177 -0.2294 0.3135 -0.4004 -0.0869
-0.1915 0.2655 0.4570 0.2022 0.1466 0.3488
-0.4083 -0.4815 -0.0732 0.1384 -0.4058 -0.2674
0.4440 -0.0507 -0.4947 -0.2001 -0.1060 -0.3061
In both samples the columns marked x1 and x2 are uniformly distributed
on [-0.5, +0.5]. (Reasonably closely, anyway: the data are set up so that
there will be one (x1,x2) in [-0.5,-0.4]x[-0.5,-0.4], one in
[-0.5,-0.4]x[-0.4,-0.3],
one in [-0.5,-0.4]x[-0.3,-0.2], and so on, for the obvious partition of
[-0.5,+0.5]x[-0.5,+0.5] into 100 smaller squares of side 0.1. So they do
fill the square, as you requested.)
Both, in fact are subsets of larger samples, and I can
send you the full files if interested --- there is not enough room here.
In both samples the three columns are connected via x3 = x1 + x2.
However, in one of the two samples x3 is in fact computed in this way,
caused by the other two, the way I use the word, whereas in the other
sample x1 and x3 are originally generated (uniformly) and then x2
is calculated as x2 = x3 - x1, in other words, x2 is the _effect_.
Can you tell them apart?
> Sampling is a type of perception and like all perception, the instrument is
> a construction. The eyes do not allow us to see many wave lengths. We are
> subject to certain illusions. The eyes are not perfect. No sampling strategy
> is perfect either. Only God in his omniscience has perfect perception. We
> ain't him. Neither is the normal distribution.
> When we collect an approximately equal number AND a sufficient number of
> observations so that we can see the combinations of all the possible values
> of the causes, then we get a less distorted view of how those causes can
> combine. The manifold is a map or prototype of such structure. A cause can
> be expressed in data but unless we can see it, we can not make much sense of
> it. This is why scientists search long and hard to fill out the ranges of
> their observations in experimental science. Normal distributions do not
> reflect the combinations of the similar extremes of causes. You do not see
> normally distributed cell sizes across the factors of an ANOVA. We need
> something else to see what happens in the extremes of the
> cross-tabulation/conjunction of causes. This something else is a manifold,
> which is approximated by uniform samples of the causes.
>
> Bill
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
