Appendix A. Values of the 95% quantiles for absolute loadings of the first variable in the first five principal components for each correlation structure considered in this study (Fig. 1) and a spherical correlation matrix.
Note that values across components
would change according to the chosen variable. Samples were based on normally
distributed samples containing N observations. One-thousand samples
were used in each case. Parametric correlation coefficients r (
= 0.05)
are shown according to sample size. First, note that in all cases, values
change along axes. Second, values in the spherical population are always
larger than the correspondent tabled correlation value, indicating that the
latter may be too liberal. Our results (Tables 2 and 3) show that this
is in fact the case. Thus, standard tabled values are in fact inappropriate
for asssesing eigenvector significance.
| N = 30
(r = 0.361) |
N = 40
(r = 0.312) |
|||||||||||
| Component |
Component |
|||||||||||
| 1 |
2 |
3 |
4 |
5 |
1 |
2 |
3 |
4 |
5 |
|||
| Correlation
matrix |
Nine
variables |
|||||||||||
| Spherical | 0.763 |
0.730 |
0.709 |
0.644 |
0.600 |
0.735 |
0.717 |
0.685 |
0.665 |
0.635 |
||
| 1 |
0.936 |
0.493 |
0.323 |
0.397 |
0.342 |
0.937 |
0.493 |
0.292 |
0.391 |
0.331 |
||
| 2 |
0.903 |
0.588 |
0.372 |
0.396 |
0.332 |
0.889 |
0.570 |
0.351 |
0.403 |
0.339 |
||
| 3 |
0.911 |
0.533 |
0.361 |
0.385 |
0.343 |
0.900 |
0.520 |
0.341 |
0.380 |
0.334 |
||
| 4 |
0.867 |
0.660 |
0.480 |
0.574 |
0.513 |
0.846 |
0.593 |
0.422 |
0.580 |
0.516 |
||
| 5 |
0.839 |
0.655 |
0.515 |
0.539 |
0.513 |
0.822 |
0.605 |
0.482 |
0.568 |
0.503 |
||
| 6 |
0.810 |
0.706 |
0.626 |
0.610 |
0.563 |
0.799 |
0.691 |
0.572 |
0.613 |
0.580 |
||
| 7 |
0.941 |
0.612 |
0.383 |
0.238 |
0.226 |
0.936 |
0.516 |
0.358 |
0.196 |
0.193 |
||
| 8 |
0.949 |
0.361 |
0.250 |
0.232 |
0.258 |
0.946 |
0.325 |
0.223 |
0.195 |
0.222 |
||
| 9 |
0.945 |
0.399 |
0.251 |
0.228 |
0.262 |
0.944 |
0.362 |
0.230 |
0.195 |
0.205 |
||
| 10 |
0.939 |
0.572 |
0.275 |
0.247 |
0.240 |
0.941 |
0.504 |
0.245 |
0.209 |
0.210 |
||
| 11 |
0.874 |
0.708 |
0.478 |
0.427 |
0.449 |
0.864 |
0.680 |
0.429 |
0.406 |
0.420 |
||
| 12 |
0.952 |
0.306 |
0.267 |
0.244 |
0.224 |
0.949 |
0.251 |
0.234 |
0.206 |
0.206 |
||
| 13 |
0.883 |
0.546 |
0.446 |
0.458 |
0.419 |
0.875 |
0.449 |
0.401 |
0.382 |
0.373 |
||
| 14 |
0.822 |
0.726 |
0.591 |
0.582 |
0.507 |
0.818 |
0.663 |
0.555 |
0.549 |
0.514 |
||
| N = 60
(r = 0.254) |
N = 80
(r = 0.220) |
|||||||||||
| Eighteen
variables |
||||||||||||
| Spherical |
0.603 |
0.587 |
0.573 |
0.575 |
0.538 |
0.581 |
0.548 |
0.552 |
0.532 |
0.506 |
||
| 1 |
0.925 |
0.410 |
0.241 |
0.303 |
0.293 |
0.924 |
0.384 |
0.213 |
0.297 |
0.266 |
||
| 2 |
0.866 |
0.533 |
0.307 |
0.317 |
0.277 |
0.856 |
0.513 |
0.278 |
0.279 |
0.272 |
||
| 3 |
0.886 |
0.485 |
0.290 |
0.299 |
0.279 |
0.876 |
0.460 |
0.276 |
0.296 |
0.271 |
||
| 4 |
0.817 |
0.471 |
0.297 |
0.480 |
0.422 |
0.814 |
0.435 |
0.278 |
0.442 |
0.407 |
||
| 5 |
0.770 |
0.523 |
0.341 |
0.476 |
0.408 |
0.761 |
0.510 |
0.317 |
0.435 |
0.435 |
||
| 6 |
0.729 |
0.529 |
0.395 |
0.536 |
0.485 |
0.728 |
0.502 |
0.346 |
0.496 |
0.464 |
||
| 7 |
0.931 |
0.380 |
0.233 |
0.146 |
0.148 |
0.927 |
0.340 |
0.211 |
0.134 |
0.127 |
||
| 8 |
0.935 |
0.236 |
0.150 |
0.145 |
0.156 |
0.933 |
0.216 |
0.129 |
0.122 |
0.134 |
||
| 9 |
0.932 |
0.313 |
0.158 |
0.151 |
0.156 |
0.927 |
0.292 |
0.148 |
0.122 |
0.132 |
||
| 10 |
0.933 |
0.366 |
0.160 |
0.141 |
0.142 |
0.931 |
0.346 |
0.127 |
0.130 |
0.130 |
||
| 11 |
0.836 |
0.426 |
0.315 |
0.282 |
0.304 |
0.824 |
0.370 |
0.269 |
0.252 |
0.271 |
||
| 12 |
0.938 |
0.154 |
0.138 |
0.146 |
0.141 |
0.937 |
0.124 |
0.125 |
0.129 |
0.124 |
||
| 13 |
0.839 |
0.289 |
0.281 |
0.283 |
0.280 |
0.829 |
0.249 |
0.255 |
0.253 |
0.261 |
||
| 14 |
0.762 |
0.422 |
0.398 |
0.393 |
0.406 |
0.750 |
0.398 |
0.393 |
0.394 |
0.367 |
||