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This link concerns the following paper: MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4, 84-99. In this paper we conducted factor analyses on 9 population correlation matrices. Those 9 matrices and corresponding factor solutions are made available here in a file. Click here to download the compressed text file. Population Correlation Matrix
10 variables, Three Factors, High Communality
1.000
.087 1.000
.001 -.070 1.000
.635 .352 .072 1.000
-.077 .147 .639 .073 1.000
-.084 .623 -.039 .197 .212 1.000
-.028 -.064 .799 .046 .646 -.024 1.000
.047 -.059 .746 .115 .591 -.043 .744 1.000
.672 .101 .194 .738 .075 -.082 .162 .232 1.000
.517 .353 .101 .688 .119 .234 .081 .134 .614 1.000
Rotated ML solution (Direct Quartimin)
1 2 3
1 -0.094 0.785 -0.134
2 -0.048 0.140 0.743
3 0.890 0.025 -0.085
4 -0.001 0.846 0.196
5 0.740 -0.072 0.227
6 0.018 -0.081 0.844
7 0.895 -0.012 -0.066
8 0.824 0.083 -0.090
9 0.110 0.886 -0.145
10 0.052 0.694 0.246
Communality
1 2 3 4 5 6 7
0.600 0.600 0.800 0.800 0.600 0.700 0.800
8 9 10
0.300 0.800 0.600
10 variables, Three Factors, Wide Communality
1.000
.347 1.000
-.071 -.010 1.000
.208 .093 .540 1.000
.082 .286 .190 .054 1.000
.094 .172 .215 .139 .325 1.000
.271 .396 .094 .066 .617 .338 1.000
.051 .148 .747 .510 .404 .321 .353 1.000
.008 .202 .150 .014 .486 .256 .483 .316 1.000
.011 .250 .132 -.022 .593 .304 .593 .342 .488 1.000
Rotated ML solution (Direct Quartimin)
1 2 3
1 -0.067 0.027 0.782
2 0.289 -0.033 0.418
3 0.051 0.881 -0.198
4 -0.158 0.682 0.212
5 0.766 0.032 0.007
6 0.363 0.165 0.058
7 0.753 -0.045 0.263
8 0.328 0.768 -0.062
9 0.641 0.007 -0.070
10 0.796 -0.052 -0.079
Communality
1 2 3 4 5 6 7
0.600 0.300 0.800 0.500 0.600 0.200 0.700
8 9 10
0.800 0.400 0.600
10 variables, Three Factors, Low Communality
1.000
-.008 1.000
.186 .064 1.000
.245 -.008 .231 1.000
.179 .119 .193 .220 1.000
.038 .341 .093 .048 .142 1.000
-.019 .227 .162 -.019 .060 .186 1.000
.276 .065 .252 .338 .271 .118 -.006 1.000
.198 .027 .184 .243 .188 .068 -.007 .282 1.000
-.011 .078 .149 -.009 .021 .061 .222 -.024 -.012 1.000
Rotated ML solution (Direct Quartimin)
1 2 3
1 0.452 -0.049 -0.015
2 -0.035 0.629 0.027
3 0.412 -0.050 0.345
4 0.554 -0.060 -0.009
5 0.399 0.149 0.009
6 0.072 0.530 0.010
7 -0.060 0.217 0.447
8 0.623 0.070 -0.073
9 0.447 0.013 -0.032
10 -0.035 -0.023 0.455
Communality
1 2 3 4 5 6 7
0.200 0.400 0.300 0.300 0.200 0.300 0.300
8 9 10
0.400 0.200 0.200
20 variables, Three Factors, High Communality
1
.298 1
.204 .457 1
.484 .348 .479 1
.141 .510 .590 .415 1
.630 .258 .292 .580 .208 1
.380 .679 .221 .254 .263 .301 1
.631 .338 .339 .596 .264 .696 .360 1
-.035 .398 .550 .295 .573 .035 .115 .089 1
.233 .470 -.055 -.002 .001 .110 .584 .150 -.113 1
.330 .789 .529 .426 .568 .318 .640 .395 .455 .395 1
.450 .729 .275 .329 .310 .380 .745 .441 .144 .598 .698 1
.607 .143 .247 .559 .149 .691 .198 .674 -.010 .025 .210 .273
1
.092 .672 .205 .050 .295 -.010 .617 .065 .227 .540 .615 .632
-.123 1
.143 .473 -.108 -.103 -.031 -.004 .588 .042 -.126 .639 .380 .590
-.096 .596 1
.205 .703 .239 .144 .313 .113 .665 .186 .214 .561 .655 .693
.000 .689 .597 1
.660 .385 .409 .657 .331 .736 .380 .746 .151 .137 .452 .468
.711 .080 .021 .205 1
-.111 .365 .514 .224 .547 -.049 .078 .004 .596 -.127 .415 .096
-.094 .227 -.126 .199 .061 1
.256 .508 .692 .570 .673 .363 .241 .413 .623 -.079 .596 .306
.315 .208 -.147 .252 .495 .578 1
.554 .377 .401 .582 .339 .623 .346 .638 .188 .118 .438 .423
.595 .105 .020 .209 .689 .113 .480 1
Rotated ML solution (Direct Quartimin)
1 2 3
1 0.754 0.156 -0.157
2 0.106 0.688 0.409
3 0.226 -0.004 0.689
4 0.651 -0.069 0.315
5 0.100 0.100 0.719
6 0.851 -0.013 -0.054
7 0.214 0.761 0.019
8 0.821 0.059 0.009
9 -0.099 -0.008 0.794
10 0.032 0.771 -0.258
11 0.182 0.584 0.489
12 0.302 0.768 0.044
13 0.872 -0.139 -0.098
14 -0.201 0.805 0.207
15 -0.116 0.848 -0.268
16 -0.046 0.801 0.172
17 0.857 0.047 0.087
18 -0.202 -0.007 0.800
19 0.301 -0.036 0.780
20 0.708 0.058 0.152
Communality
1 2 3 4 5 6 7
0.600 0.800 0.700 0.600 0.600 0.700 0.700
8 9 10 11 12 13 14
0.700 0.600 0.600 0.800 0.800 0.700 0.700
15 16 17 18 19 20
0.700 0.700 0.800 0.600 0.800 0.600
20 variables, Three Factors, Wide Communality
1
.394 1
.310 .164 1
.151 .029 .188 1
.037 -.034 .120 .687 1
.148 .113 .097 .450 .456 1
.197 .298 -.040 -.053 -.029 .260 1
.318 .173 .196 .124 .052 .051 -.044 1
.378 .170 .301 .642 .575 .399 -.051 .255 1
.186 .288 -.041 -.020 .007 .283 .798 -.050 -.030 1
.453 .304 .251 .395 .330 .351 .273 .226 .496 .282 1
.217 .205 .102 .535 .551 .551 .514 .045 .468 .542 .488
1
.311 .163 .198 .153 .082 .066 -.058 .199 .276 -.062 .231
.059 1
.308 .279 .090 -.026 -.060 .127 .418 .096 .071 .410 .259
.253 .085 1
.189 .296 -.051 -.103 -.080 .226 .797 -.051 -.095 .794 .245
.471 -.067 .419 1
.166 .271 -.056 -.111 -.087 .202 .745 -.054 -.106 .742 .216
.429 -.070 .388 .748 1
.111 .039 .112 .372 .360 .246 -.005 .080 .353 .011 .232
.298 .094 .008 -.032 -.038 1
.089 .106 .041 .429 .457 .434 .379 -.007 .339 .404 .336
.624 .006 .155 .345 .314 .234 1
.409 .215 .284 .482 .408 .314 .017 .254 .577 .029 .455
.381 .266 .126 -.016 -.029 .272 .260 1
.314 .168 .200 .173 .104 .087 -.040 .198 .291 -.042 .246
.089 .199 .093 -.050 -.054 .105 .030 .278 1
Rotated ML solution (Direct Quartimin)
1 2 3
1 0.225 -0.069 0.745
2 0.344 -0.086 0.427
3 -0.059 0.064 0.425
4 -0.185 0.806 0.095
5 -0.165 0.857 -0.077
6 0.203 0.576 0.001
7 0.888 0.060 -0.066
8 -0.051 -0.023 0.453
9 -0.156 0.610 0.434
10 0.881 0.108 -0.089
11 0.249 0.346 0.447
12 0.466 0.723 -0.031
13 -0.072 0.014 0.442
14 0.479 -0.076 0.261
15 0.896 -0.001 -0.066
16 0.840 -0.014 -0.075
17 -0.071 0.418 0.085
18 0.332 0.615 -0.133
19 -0.048 0.407 0.480
20 -0.056 0.043 0.434
Communality
1 2 3 4 5 6 7
0.300 0.300 0.200 0.700 0.700 0.400 0.800
8 9 10 11 12 13 14
0.200 0.700 0.800 0.500 0.800 0.200 0.300
15 16 17 18 19 20
0.800 0.700 0.200 0.500 0.500 0.200
20 variables, 3 Factors, Low Communality
1
.238 1
.003 .033 1
.209 .161 .296 1
.205 .211 .178 .287 1
.291 .213 .155 .305 .269 1
.108 .174 .194 .255 .285 .215 1
.356 .278 -.009 .181 .262 .282 .198 1
.113 .121 .279 .334 .253 .235 .250 .120 1
.077 .195 .097 .149 .277 .165 .311 .235 .175 1
.237 .258 .145 .276 .338 .290 .324 .330 .247 .351 1
.218 .257 .076 .199 .311 .248 .303 .338 .185 .371 .388
1
.286 .241 -.015 .140 .230 .231 .184 .344 .098 .232 .295
.309 1
.055 .173 -.047 -.003 .188 .078 .222 .228 .038 .364 .280
.336 .232 1
.002 .149 .157 .168 .264 .138 .318 .157 .206 .386 .322
.329 .165 .325 1
-.052 .075 .050 .032 .133 .031 .183 .075 .077 .262 .180
.204 .091 .251 .268 1
.103 .129 .272 .324 .263 .230 .267 .129 .298 .208 .265
.211 .110 .077 .238 .105 1
.115 .098 .224 .280 .198 .200 .184 .101 .242 .109 .186
.131 .077 -.004 .131 .033 .235 1
.016 .067 .232 .239 .188 .144 .208 .045 .234 .163 .183
.140 .042 .055 .202 .098 .238 .180 1
-.006 .079 .272 .269 .227 .158 .262 .051 .275 .225 .228
.184 .051 .100 .273 .146 .284 .205 .243 1
Rotated ML solution (Direct Quartimin)
1 2 3
1 0.016 0.654 -0.206
2 0.033 0.392 0.109
3 0.581 -0.132 -0.051
4 0.574 0.210 -0.132
5 0.301 0.276 0.173
6 0.291 0.414 -0.073
7 0.317 0.115 0.302
8 -0.055 0.608 0.109
9 0.525 0.065 0.005
10 0.096 0.123 0.549
11 0.219 0.352 0.296
12 0.072 0.358 0.396
13 -0.071 0.498 0.166
14 -0.187 0.154 0.609
15 0.214 -0.030 0.546
16 0.027 -0.079 0.455
17 0.501 0.056 0.075
18 0.432 0.089 -0.071
19 0.426 -0.070 0.100
20 0.489 -0.118 0.195
Communality
1 2 3 4 5 6 7
0.400 0.200 0.300 0.400 0.300 0.300 0.300
8 9 10 11 12 13 14
0.400 0.300 0.400 0.400 0.400 0.300 0.400
15 16 17 18 19 20
0.400 0.200 0.300 0.200 0.200 0.300
20 variables, 7 Factors, High Communality
1
-.052 1
.401 .019 1
.012 .561 .229 1
.682 .189 .401 .240 1
-.053 .745 .015 .586 .193 1
.083 -.060 .408 .082 .064 -.087 1
.084 .227 .454 .259 .213 .237 .195 1
-.054 .629 .146 .576 .252 .650 .051 .393 1
.070 .151 .322 .174 .158 .115 .548 .339 .307 1
.014 .168 .166 .222 .083 .141 .128 .174 .069 .362 1
.076 -.113 .590 .050 .043 -.131 .578 .448 .001 .520 .244 1
.025 .26 .191 .152 .024 .317 -.040 .276 .053 -.067 .112 .206
1
.134 .366 -.064 .202 .122 .417 -.114 -.091 .033 -.099 .153 -.145
.389 1
.354 .340 .288 .312 .363 .361 .272 .101 .180 .319 .255 .203
.239 .425 1
-.089 .456 -.042 .271 -.039 .518 -.103 .074 .136 -.064 .201 -.021
.542 .583 .360 1
-.043 .208 .036 .216 -.004 .215 -.076 .034 -.019 .014 .596 .041
.258 .324 .220 .381 1
.031 .281 .343 .344 .120 .275 .558 .214 .317 .603 .228 .462
.054 .107 .457 .141 .056 1
.508 .467 .217 .417 .553 .509 -.038 .042 .275 .001 .148 -.126
.257 .525 .566 .402 .240 .205 1
.214 .043 .314 .266 .211 .031 .093 .012 -.068 -.004 .497 .155
.071 .155 .253 .105 .477 .132 .315 1
Rotated ML solution (Direct Quartimin)
1 2 3 4 5 6 7
1 -0.225 -0.027 0.913 -0.006 -0.038 0.044 0.003
2 0.728 -0.003 0.006 0.213 0.045 -0.041 -0.087
3 0.007 0.300 0.323 -0.004 -0.009 0.496 0.302
4 0.716 0.091 -0.002 -0.031 0.092 0.032 0.238
5 0.150 -0.067 0.811 -0.121 0.010 0.103 -0.016
6 0.758 -0.026 0.005 0.293 0.002 -0.032 -0.073
7 -0.096 0.769 -0.031 -0.066 -0.063 0.058 0.065
8 0.252 0.025 0.078 0.057 0.053 0.694 -0.096
9 0.885 0.022 0.018 -0.178 -0.072 0.178 -0.112
10 0.074 0.666 0.072 -0.179 0.227 0.116 -0.402
11 -0.021 0.064 0.001 -0.070 0.904 0.071 -0.124
12 -0.228 0.591 -0.073 0.114 0.067 0.514 0.089
13 -0.024 -0.065 -0.022 0.730 0.003 0.354 0.038
14 0.042 0.020 0.157 0.625 0.089 -0.280 -0.019
15 0.084 0.432 0.359 0.333 0.086 -0.191 -0.008
16 0.151 0.010 -0.114 0.751 0.110 -0.051 -0.022
17 0.005 -0.119 -0.080 0.204 0.693 -0.024 0.092
18 0.240 0.797 -0.056 0.042 -0.008 -0.097 0.021
19 0.299 -0.001 0.590 0.300 0.033 -0.223 0.125
20 0.013 0.016 0.125 -0.108 0.544 -0.045 0.517
Communality
1 2 3 4 5 6 7
0.800 0.700 0.700 0.600 0.700 0.800 0.600
8 9 10 11 12 13 14
0.600 0.800 0.800 0.800 0.800 0.600 0.600
15 16 17 18 19 20
0.600 0.700 0.600 0.700 0.800 0.700
20 variables, 7 Factors, wide Communality
1
-.031 1
.193 -.054 1
-.017 -.076 .259 1
.508 -.002 .476 .073 1
-.048 .307 .089 .264 .025 1
.058 -.100 .017 .461 .066 -.015 1
.111 -.066 .323 .546 .253 .165 .681 1
-.032 .409 .222 .235 .145 .617 .072 .264 1
-.090 .009 .034 .426 -.037 .010 .477 .344 .142 1
.091 .087 .065 .220 .119 .111 .175 .248 .182 .431 1
.403 .026 .520 .080 .569 .011 .131 .307 .211 .060 .120 1
.106 -.062 .383 .382 .262 .103 .372 .491 .196 .189 .011 .311
1
.115 .097 .521 .412 .324 .451 .057 .374 .491 -.040 -.029 .319
.374 1
.132 .140 .342 .255 .276 .372 .074 .327 .435 .001 .182 .270
.238 .467 1
.049 .112 .190 .453 .099 .509 .103 .320 .424 .025 .140 .034
.209 .520 .390 1
-.013 -.057 .134 .437 .002 .116 .093 .113 .058 .382 .303 -.020
.103 .155 .074 .243 1
.220 -.108 .130 .560 .199 .052 .652 .592 .082 .494 .277 .198
.361 .172 .138 .233 .307 1
.511 -.043 .229 .133 .443 .017 .045 .118 .001 .025 .179 .339
.121 .176 .155 .147 .164 .270 1
-.015 .105 .075 .105 .031 .110 -.047 -.025 .173 .235 .274 .053
-.011 .043 .066 .062 .219 .057 .064 1
Rotated ML solution (Direct Quartimin)
1 2 3 4 5 6 7
1 0.033 -0.049 0.782 -0.014 -0.001 -0.085 -0.008
2 -0.058 -0.091 0.008 -0.032 0.550 -0.032 0.014
3 -0.091 0.837 0.028 0.047 -0.100 0.092 0.027
4 0.447 0.110 -0.058 0.384 -0.083 0.388 -0.008
5 0.012 0.395 0.533 -0.057 0.040 -0.093 0.045
6 -0.005 -0.063 -0.024 0.475 0.516 0.048 -0.010
7 0.931 -0.108 -0.006 -0.075 0.002 -0.088 0.021
8 0.725 0.239 -0.055 0.209 -0.049 -0.213 0.194
9 0.118 0.165 -0.073 0.169 0.772 0.011 0.009
10 0.508 -0.003 -0.121 -0.305 0.129 0.463 0.181
11 0.048 -0.049 0.031 0.051 -0.040 0.021 0.884
12 0.102 0.541 0.353 -0.224 0.128 -0.088 0.035
13 0.396 0.386 0.001 0.068 -0.002 0.028 -0.115
14 0.014 0.471 0.043 0.474 0.184 0.088 -0.159
15 0.028 0.270 0.061 0.353 0.192 -0.121 0.170
16 0.060 -0.028 0.067 0.697 0.130 0.092 0.044
17 0.002 0.019 0.039 0.176 -0.126 0.624 0.099
18 0.703 -0.106 0.265 0.061 -0.048 0.218 0.021
19 -0.020 -0.017 0.684 0.088 -0.055 0.141 0.035
20 -0.099 0.063 0.000 -0.086 0.160 0.299 0.176
Communality
1 2 3 4 5 6 7
0.600 0.300 0.700 0.700 0.600 0.600 0.800
8 9 10 11 12 13 14
0.800 0.800 0.700 0.800 0.600 0.400 0.700
15 16 17 18 19 20
0.400 0.600 0.500 0.700 0.500 0.200
20 variables, 7 Factors, Low Communality
1
.021 1
-.050 .025 1
.072 .191 .061 1
.252 .026 -.011 -.024 1
.123 .135 .013 .315 .020 1
.016 .144 .148 .281 -.001 .205 1
-.001 .107 .253 .186 .008 .089 .256 1
-.036 .252 .007 .201 .008 .129 .137 .087 1
-.019 .016 .119 .122 -.027 .009 .180 .182 .008 1
.079 .034 .023 .129 .035 .060 .111 .077 .098 .129 1
.030 -.003 .225 .107 -.001 .112 .086 .151 .011 .056 .076
1
.118 -.026 .072 .095 .044 .202 .069 .048 -.058 .005 .040
.161 1
-.016 -.030 .008 .087 -.043 .169 .114 .041 -.070 .059 .021
.015 .123 1
.141 .009 .017 .183 .041 .293 .153 .065 -.044 .046 .061
.087 .211 .207 1
-.004 .066 .153 .137 .004 .157 .206 .193 .048 .111 .043
.092 .101 .133 .154 1
-.031 .019 -.000 .116 -.034 .134 .125 .044 .112 .110 .185
.062 .086 .135 .140 .106 1
.038 .010 -.012 .078 .016 .170 .122 .045 -.025 .045 .018
-.030 .104 .183 .201 .142 .126 1
.312 -.008 -.042 -.031 .231 .014 .001 .003 -.060 .007 .055
-.043 .052 -.009 .080 .010 -.023 .056 1
.088 -.051 .122 .098 .017 .118 .036 .056 .007 .060 .177
.289 .184 .030 .119 .035 .178 -.025 -.003 1
Rotated ML solution (Direct Quartimin)
1 2 3 4 5 6 7
1 -0.026 0.580 -0.078 0.082 -0.040 0.004 0.162
2 -0.030 0.032 0.069 -0.075 0.385 -0.045 0.118
3 -0.042 -0.036 0.504 0.211 -0.008 -0.073 -0.081
4 0.041 -0.055 0.059 0.045 0.193 0.073 0.501
5 -0.014 0.447 0.028 0.013 0.066 -0.012 -0.082
6 0.346 0.018 -0.090 0.189 0.211 -0.090 0.308
7 0.160 -0.004 0.315 -0.076 0.130 0.102 0.214
8 0.004 0.027 0.502 0.007 0.065 0.025 0.087
9 -0.083 -0.037 -0.017 -0.002 0.615 0.115 -0.016
10 -0.007 -0.020 0.281 -0.102 -0.115 0.275 0.111
11 -0.052 0.090 0.006 0.076 0.046 0.405 0.062
12 -0.064 -0.035 0.215 0.482 -0.007 -0.005 0.026
13 0.244 0.084 0.004 0.305 -0.059 -0.048 0.054
14 0.418 -0.082 0.007 -0.011 -0.103 0.038 0.044
15 0.419 0.097 -0.031 0.132 -0.058 0.000 0.175
16 0.291 0.008 0.298 0.010 0.080 -0.003 -0.026
17 0.265 -0.081 -0.072 0.099 0.123 0.424 -0.104
18 0.446 0.048 0.021 -0.095 -0.001 0.022 -0.022
19 0.040 0.543 0.021 -0.082 -0.059 0.053 -0.041
20 -0.064 0.012 -0.025 0.553 -0.050 0.265 0.020
Communality
1 2 3 4 5 6 7
0.400 0.200 0.300 0.400 0.200 0.400 0.300
8 9 10 11 12 13 14
0.300 0.400 0.200 0.200 0.300 0.200 0.200
15 16 17 18 19 20
0.300 0.200 0.300 0.200 0.300 0.400
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