Main page: https://www.rdocumentation.org/packages/datasets/versions/3.6.2/topics/Harman74.cor
head(Harman74.cor)## $cov
## VisualPerception Cubes PaperFormBoard Flags
## VisualPerception 1.000 0.318 0.403 0.468
## Cubes 0.318 1.000 0.317 0.230
## PaperFormBoard 0.403 0.317 1.000 0.305
## Flags 0.468 0.230 0.305 1.000
## GeneralInformation 0.321 0.285 0.247 0.227
## PargraphComprehension 0.335 0.234 0.268 0.327
## SentenceCompletion 0.304 0.157 0.223 0.335
## WordClassification 0.332 0.157 0.382 0.391
## WordMeaning 0.326 0.195 0.184 0.325
## Addition 0.116 0.057 -0.075 0.099
## Code 0.308 0.150 0.091 0.110
## CountingDots 0.314 0.145 0.140 0.160
## StraightCurvedCapitals 0.489 0.239 0.321 0.327
## WordRecognition 0.125 0.103 0.177 0.066
## NumberRecognition 0.238 0.131 0.065 0.127
## FigureRecognition 0.414 0.272 0.263 0.322
## ObjectNumber 0.176 0.005 0.177 0.187
## NumberFigure 0.368 0.255 0.211 0.251
## FigureWord 0.270 0.112 0.312 0.137
## Deduction 0.365 0.292 0.297 0.339
## NumericalPuzzles 0.369 0.306 0.165 0.349
## ProblemReasoning 0.413 0.232 0.250 0.380
## SeriesCompletion 0.474 0.348 0.383 0.335
## ArithmeticProblems 0.282 0.211 0.203 0.248
## GeneralInformation PargraphComprehension
## VisualPerception 0.321 0.335
## Cubes 0.285 0.234
## PaperFormBoard 0.247 0.268
## Flags 0.227 0.327
## GeneralInformation 1.000 0.622
## PargraphComprehension 0.622 1.000
## SentenceCompletion 0.656 0.722
## WordClassification 0.578 0.527
## WordMeaning 0.723 0.714
## Addition 0.311 0.203
## Code 0.344 0.353
## CountingDots 0.215 0.095
## StraightCurvedCapitals 0.344 0.309
## WordRecognition 0.280 0.292
## NumberRecognition 0.229 0.251
## FigureRecognition 0.187 0.291
## ObjectNumber 0.208 0.273
## NumberFigure 0.263 0.167
## FigureWord 0.190 0.251
## Deduction 0.398 0.435
## NumericalPuzzles 0.318 0.263
## ProblemReasoning 0.441 0.386
## SeriesCompletion 0.435 0.431
## ArithmeticProblems 0.420 0.433
## SentenceCompletion WordClassification WordMeaning
## VisualPerception 0.304 0.332 0.326
## Cubes 0.157 0.157 0.195
## PaperFormBoard 0.223 0.382 0.184
## Flags 0.335 0.391 0.325
## GeneralInformation 0.656 0.578 0.723
## PargraphComprehension 0.722 0.527 0.714
## SentenceCompletion 1.000 0.619 0.685
## WordClassification 0.619 1.000 0.532
## WordMeaning 0.685 0.532 1.000
## Addition 0.246 0.285 0.170
## Code 0.232 0.300 0.280
## CountingDots 0.181 0.271 0.113
## StraightCurvedCapitals 0.345 0.395 0.280
## WordRecognition 0.236 0.252 0.260
## NumberRecognition 0.172 0.175 0.248
## FigureRecognition 0.180 0.296 0.242
## ObjectNumber 0.228 0.255 0.274
## NumberFigure 0.159 0.250 0.208
## FigureWord 0.226 0.274 0.274
## Deduction 0.451 0.427 0.446
## NumericalPuzzles 0.314 0.362 0.266
## ProblemReasoning 0.396 0.357 0.483
## SeriesCompletion 0.405 0.501 0.504
## ArithmeticProblems 0.437 0.388 0.424
## Addition Code CountingDots StraightCurvedCapitals
## VisualPerception 0.116 0.308 0.314 0.489
## Cubes 0.057 0.150 0.145 0.239
## PaperFormBoard -0.075 0.091 0.140 0.321
## Flags 0.099 0.110 0.160 0.327
## GeneralInformation 0.311 0.344 0.215 0.344
## PargraphComprehension 0.203 0.353 0.095 0.309
## SentenceCompletion 0.246 0.232 0.181 0.345
## WordClassification 0.285 0.300 0.271 0.395
## WordMeaning 0.170 0.280 0.113 0.280
## Addition 1.000 0.484 0.585 0.408
## Code 0.484 1.000 0.428 0.535
## CountingDots 0.585 0.428 1.000 0.512
## StraightCurvedCapitals 0.408 0.535 0.512 1.000
## WordRecognition 0.172 0.350 0.131 0.195
## NumberRecognition 0.154 0.240 0.173 0.139
## FigureRecognition 0.124 0.314 0.119 0.281
## ObjectNumber 0.289 0.362 0.278 0.194
## NumberFigure 0.317 0.350 0.349 0.323
## FigureWord 0.190 0.290 0.110 0.263
## Deduction 0.173 0.202 0.246 0.241
## NumericalPuzzles 0.405 0.399 0.355 0.425
## ProblemReasoning 0.160 0.304 0.193 0.279
## SeriesCompletion 0.262 0.251 0.350 0.382
## ArithmeticProblems 0.531 0.412 0.414 0.358
## WordRecognition NumberRecognition FigureRecognition
## VisualPerception 0.125 0.238 0.414
## Cubes 0.103 0.131 0.272
## PaperFormBoard 0.177 0.065 0.263
## Flags 0.066 0.127 0.322
## GeneralInformation 0.280 0.229 0.187
## PargraphComprehension 0.292 0.251 0.291
## SentenceCompletion 0.236 0.172 0.180
## WordClassification 0.252 0.175 0.296
## WordMeaning 0.260 0.248 0.242
## Addition 0.172 0.154 0.124
## Code 0.350 0.240 0.314
## CountingDots 0.131 0.173 0.119
## StraightCurvedCapitals 0.195 0.139 0.281
## WordRecognition 1.000 0.370 0.412
## NumberRecognition 0.370 1.000 0.325
## FigureRecognition 0.412 0.325 1.000
## ObjectNumber 0.341 0.345 0.324
## NumberFigure 0.201 0.334 0.344
## FigureWord 0.206 0.192 0.258
## Deduction 0.302 0.272 0.388
## NumericalPuzzles 0.183 0.232 0.348
## ProblemReasoning 0.243 0.246 0.283
## SeriesCompletion 0.242 0.256 0.360
## ArithmeticProblems 0.304 0.165 0.262
## ObjectNumber NumberFigure FigureWord Deduction
## VisualPerception 0.176 0.368 0.270 0.365
## Cubes 0.005 0.255 0.112 0.292
## PaperFormBoard 0.177 0.211 0.312 0.297
## Flags 0.187 0.251 0.137 0.339
## GeneralInformation 0.208 0.263 0.190 0.398
## PargraphComprehension 0.273 0.167 0.251 0.435
## SentenceCompletion 0.228 0.159 0.226 0.451
## WordClassification 0.255 0.250 0.274 0.427
## WordMeaning 0.274 0.208 0.274 0.446
## Addition 0.289 0.317 0.190 0.173
## Code 0.362 0.350 0.290 0.202
## CountingDots 0.278 0.349 0.110 0.246
## StraightCurvedCapitals 0.194 0.323 0.263 0.241
## WordRecognition 0.341 0.201 0.206 0.302
## NumberRecognition 0.345 0.334 0.192 0.272
## FigureRecognition 0.324 0.344 0.258 0.388
## ObjectNumber 1.000 0.448 0.324 0.262
## NumberFigure 0.448 1.000 0.358 0.301
## FigureWord 0.324 0.358 1.000 0.167
## Deduction 0.262 0.301 0.167 1.000
## NumericalPuzzles 0.173 0.357 0.331 0.413
## ProblemReasoning 0.273 0.317 0.342 0.463
## SeriesCompletion 0.287 0.272 0.303 0.509
## ArithmeticProblems 0.326 0.405 0.374 0.366
## NumericalPuzzles ProblemReasoning SeriesCompletion
## VisualPerception 0.369 0.413 0.474
## Cubes 0.306 0.232 0.348
## PaperFormBoard 0.165 0.250 0.383
## Flags 0.349 0.380 0.335
## GeneralInformation 0.318 0.441 0.435
## PargraphComprehension 0.263 0.386 0.431
## SentenceCompletion 0.314 0.396 0.405
## WordClassification 0.362 0.357 0.501
## WordMeaning 0.266 0.483 0.504
## Addition 0.405 0.160 0.262
## Code 0.399 0.304 0.251
## CountingDots 0.355 0.193 0.350
## StraightCurvedCapitals 0.425 0.279 0.382
## WordRecognition 0.183 0.243 0.242
## NumberRecognition 0.232 0.246 0.256
## FigureRecognition 0.348 0.283 0.360
## ObjectNumber 0.173 0.273 0.287
## NumberFigure 0.357 0.317 0.272
## FigureWord 0.331 0.342 0.303
## Deduction 0.413 0.463 0.509
## NumericalPuzzles 1.000 0.374 0.451
## ProblemReasoning 0.374 1.000 0.503
## SeriesCompletion 0.451 0.503 1.000
## ArithmeticProblems 0.448 0.375 0.434
## ArithmeticProblems
## VisualPerception 0.282
## Cubes 0.211
## PaperFormBoard 0.203
## Flags 0.248
## GeneralInformation 0.420
## PargraphComprehension 0.433
## SentenceCompletion 0.437
## WordClassification 0.388
## WordMeaning 0.424
## Addition 0.531
## Code 0.412
## CountingDots 0.414
## StraightCurvedCapitals 0.358
## WordRecognition 0.304
## NumberRecognition 0.165
## FigureRecognition 0.262
## ObjectNumber 0.326
## NumberFigure 0.405
## FigureWord 0.374
## Deduction 0.366
## NumericalPuzzles 0.448
## ProblemReasoning 0.375
## SeriesCompletion 0.434
## ArithmeticProblems 1.000
##
## $center
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
## $n.obs
## [1] 145require(stats)
(Harman74.FA <- factanal(factors = 1, covmat = Harman74.cor))##
## Call:
## factanal(factors = 1, covmat = Harman74.cor)
##
## Uniquenesses:
## VisualPerception Cubes PaperFormBoard
## 0.677 0.866 0.830
## Flags GeneralInformation PargraphComprehension
## 0.768 0.487 0.491
## SentenceCompletion WordClassification WordMeaning
## 0.500 0.514 0.474
## Addition Code CountingDots
## 0.818 0.731 0.824
## StraightCurvedCapitals WordRecognition NumberRecognition
## 0.681 0.833 0.863
## FigureRecognition ObjectNumber NumberFigure
## 0.775 0.812 0.778
## FigureWord Deduction NumericalPuzzles
## 0.816 0.612 0.676
## ProblemReasoning SeriesCompletion ArithmeticProblems
## 0.619 0.524 0.593
##
## Loadings:
## Factor1
## VisualPerception 0.569
## Cubes 0.366
## PaperFormBoard 0.412
## Flags 0.482
## GeneralInformation 0.716
## PargraphComprehension 0.713
## SentenceCompletion 0.707
## WordClassification 0.697
## WordMeaning 0.725
## Addition 0.426
## Code 0.519
## CountingDots 0.419
## StraightCurvedCapitals 0.565
## WordRecognition 0.408
## NumberRecognition 0.370
## FigureRecognition 0.474
## ObjectNumber 0.434
## NumberFigure 0.471
## FigureWord 0.429
## Deduction 0.623
## NumericalPuzzles 0.569
## ProblemReasoning 0.617
## SeriesCompletion 0.690
## ArithmeticProblems 0.638
##
## Factor1
## SS loadings 7.438
## Proportion Var 0.310
##
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 622.91 on 252 degrees of freedom.
## The p-value is 2.28e-33for(factors in 2:5) print(update(Harman74.FA, factors = factors))##
## Call:
## factanal(factors = factors, covmat = Harman74.cor)
##
## Uniquenesses:
## VisualPerception Cubes PaperFormBoard
## 0.650 0.864 0.844
## Flags GeneralInformation PargraphComprehension
## 0.778 0.375 0.316
## SentenceCompletion WordClassification WordMeaning
## 0.319 0.503 0.258
## Addition Code CountingDots
## 0.670 0.608 0.581
## StraightCurvedCapitals WordRecognition NumberRecognition
## 0.567 0.832 0.850
## FigureRecognition ObjectNumber NumberFigure
## 0.743 0.770 0.625
## FigureWord Deduction NumericalPuzzles
## 0.792 0.629 0.579
## ProblemReasoning SeriesCompletion ArithmeticProblems
## 0.634 0.539 0.553
##
## Loadings:
## Factor1 Factor2
## VisualPerception 0.506 0.306
## Cubes 0.304 0.209
## PaperFormBoard 0.297 0.260
## Flags 0.327 0.339
## GeneralInformation 0.240 0.753
## PargraphComprehension 0.171 0.809
## SentenceCompletion 0.163 0.809
## WordClassification 0.344 0.615
## WordMeaning 0.148 0.849
## Addition 0.563 0.115
## Code 0.591 0.207
## CountingDots 0.647
## StraightCurvedCapitals 0.612 0.241
## WordRecognition 0.315 0.263
## NumberRecognition 0.328 0.205
## FigureRecognition 0.457 0.218
## ObjectNumber 0.431 0.209
## NumberFigure 0.601 0.116
## FigureWord 0.399 0.222
## Deduction 0.379 0.477
## NumericalPuzzles 0.604 0.237
## ProblemReasoning 0.390 0.462
## SeriesCompletion 0.486 0.474
## ArithmeticProblems 0.544 0.389
##
## Factor1 Factor2
## SS loadings 4.573 4.548
## Proportion Var 0.191 0.190
## Cumulative Var 0.191 0.380
##
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 420.24 on 229 degrees of freedom.
## The p-value is 2.01e-13
##
## Call:
## factanal(factors = factors, covmat = Harman74.cor)
##
## Uniquenesses:
## VisualPerception Cubes PaperFormBoard
## 0.500 0.793 0.662
## Flags GeneralInformation PargraphComprehension
## 0.694 0.352 0.316
## SentenceCompletion WordClassification WordMeaning
## 0.300 0.502 0.256
## Addition Code CountingDots
## 0.200 0.586 0.494
## StraightCurvedCapitals WordRecognition NumberRecognition
## 0.569 0.838 0.848
## FigureRecognition ObjectNumber NumberFigure
## 0.643 0.780 0.635
## FigureWord Deduction NumericalPuzzles
## 0.788 0.590 0.580
## ProblemReasoning SeriesCompletion ArithmeticProblems
## 0.597 0.498 0.500
##
## Loadings:
## Factor1 Factor2 Factor3
## VisualPerception 0.176 0.656 0.198
## Cubes 0.122 0.428
## PaperFormBoard 0.145 0.563
## Flags 0.239 0.487 0.107
## GeneralInformation 0.745 0.191 0.237
## PargraphComprehension 0.780 0.249 0.118
## SentenceCompletion 0.802 0.175 0.160
## WordClassification 0.571 0.327 0.256
## WordMeaning 0.821 0.248
## Addition 0.162 -0.118 0.871
## Code 0.198 0.219 0.572
## CountingDots 0.179 0.688
## StraightCurvedCapitals 0.190 0.381 0.499
## WordRecognition 0.231 0.253 0.210
## NumberRecognition 0.158 0.299 0.195
## FigureRecognition 0.108 0.557 0.186
## ObjectNumber 0.178 0.267 0.342
## NumberFigure 0.427 0.424
## FigureWord 0.167 0.355 0.240
## Deduction 0.392 0.472 0.181
## NumericalPuzzles 0.178 0.406 0.473
## ProblemReasoning 0.382 0.473 0.182
## SeriesCompletion 0.379 0.528 0.283
## ArithmeticProblems 0.377 0.226 0.554
##
## Factor1 Factor2 Factor3
## SS loadings 3.802 3.488 3.186
## Proportion Var 0.158 0.145 0.133
## Cumulative Var 0.158 0.304 0.436
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 295.59 on 207 degrees of freedom.
## The p-value is 5.12e-05
##
## Call:
## factanal(factors = factors, covmat = Harman74.cor)
##
## Uniquenesses:
## VisualPerception Cubes PaperFormBoard
## 0.438 0.780 0.644
## Flags GeneralInformation PargraphComprehension
## 0.651 0.352 0.312
## SentenceCompletion WordClassification WordMeaning
## 0.283 0.485 0.257
## Addition Code CountingDots
## 0.240 0.551 0.435
## StraightCurvedCapitals WordRecognition NumberRecognition
## 0.491 0.646 0.696
## FigureRecognition ObjectNumber NumberFigure
## 0.549 0.598 0.593
## FigureWord Deduction NumericalPuzzles
## 0.762 0.592 0.583
## ProblemReasoning SeriesCompletion ArithmeticProblems
## 0.601 0.497 0.500
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4
## VisualPerception 0.160 0.689 0.187 0.160
## Cubes 0.117 0.436
## PaperFormBoard 0.137 0.570 0.110
## Flags 0.233 0.527
## GeneralInformation 0.739 0.185 0.213 0.150
## PargraphComprehension 0.767 0.205 0.233
## SentenceCompletion 0.806 0.197 0.153
## WordClassification 0.569 0.339 0.242 0.132
## WordMeaning 0.806 0.201 0.227
## Addition 0.167 -0.118 0.831 0.166
## Code 0.180 0.120 0.512 0.374
## CountingDots 0.210 0.716
## StraightCurvedCapitals 0.188 0.438 0.525
## WordRecognition 0.197 0.553
## NumberRecognition 0.122 0.116 0.520
## FigureRecognition 0.408 0.525
## ObjectNumber 0.142 0.219 0.574
## NumberFigure 0.293 0.336 0.456
## FigureWord 0.148 0.239 0.161 0.365
## Deduction 0.378 0.402 0.118 0.301
## NumericalPuzzles 0.175 0.381 0.438 0.223
## ProblemReasoning 0.366 0.399 0.123 0.301
## SeriesCompletion 0.369 0.500 0.244 0.239
## ArithmeticProblems 0.370 0.158 0.496 0.304
##
## Factor1 Factor2 Factor3 Factor4
## SS loadings 3.647 2.872 2.657 2.290
## Proportion Var 0.152 0.120 0.111 0.095
## Cumulative Var 0.152 0.272 0.382 0.478
##
## Test of the hypothesis that 4 factors are sufficient.
## The chi square statistic is 226.68 on 186 degrees of freedom.
## The p-value is 0.0224
##
## Call:
## factanal(factors = factors, covmat = Harman74.cor)
##
## Uniquenesses:
## VisualPerception Cubes PaperFormBoard
## 0.450 0.781 0.639
## Flags GeneralInformation PargraphComprehension
## 0.649 0.357 0.288
## SentenceCompletion WordClassification WordMeaning
## 0.277 0.485 0.262
## Addition Code CountingDots
## 0.215 0.386 0.444
## StraightCurvedCapitals WordRecognition NumberRecognition
## 0.256 0.639 0.706
## FigureRecognition ObjectNumber NumberFigure
## 0.550 0.614 0.596
## FigureWord Deduction NumericalPuzzles
## 0.764 0.521 0.564
## ProblemReasoning SeriesCompletion ArithmeticProblems
## 0.580 0.442 0.478
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4 Factor5
## VisualPerception 0.161 0.658 0.136 0.182 0.199
## Cubes 0.113 0.435 0.107
## PaperFormBoard 0.135 0.562 0.107 0.116
## Flags 0.231 0.533
## GeneralInformation 0.736 0.188 0.192 0.162
## PargraphComprehension 0.775 0.187 0.251 0.113
## SentenceCompletion 0.809 0.208 0.136
## WordClassification 0.568 0.348 0.223 0.131
## WordMeaning 0.800 0.215 0.224
## Addition 0.175 -0.100 0.844 0.176
## Code 0.185 0.438 0.451 0.426
## CountingDots 0.222 0.690 0.101 0.140
## StraightCurvedCapitals 0.186 0.425 0.458 0.559
## WordRecognition 0.197 0.557
## NumberRecognition 0.121 0.130 0.508
## FigureRecognition 0.400 0.529
## ObjectNumber 0.145 0.208 0.562
## NumberFigure 0.306 0.325 0.452
## FigureWord 0.147 0.242 0.145 0.364
## Deduction 0.370 0.452 0.139 0.287 -0.190
## NumericalPuzzles 0.170 0.402 0.439 0.230
## ProblemReasoning 0.358 0.423 0.126 0.302
## SeriesCompletion 0.360 0.549 0.256 0.223 -0.107
## ArithmeticProblems 0.371 0.185 0.502 0.307
##
## Factor1 Factor2 Factor3 Factor4 Factor5
## SS loadings 3.632 2.964 2.456 2.345 0.663
## Proportion Var 0.151 0.124 0.102 0.098 0.028
## Cumulative Var 0.151 0.275 0.377 0.475 0.503
##
## Test of the hypothesis that 5 factors are sufficient.
## The chi square statistic is 186.82 on 166 degrees of freedom.
## The p-value is 0.128Harman74.FA <- factanal(factors = 5, covmat = Harman74.cor,
rotation = "promax")
print(Harman74.FA$loadings, sort = TRUE)##
## Loadings:
## Factor1 Factor2 Factor3 Factor4 Factor5
## VisualPerception 0.831 -0.127 0.230
## Cubes 0.534
## PaperFormBoard 0.736 -0.290 0.136
## Flags 0.647 -0.104
## SeriesCompletion 0.555 0.126 0.127
## GeneralInformation 0.764
## PargraphComprehension 0.845 -0.140 0.140
## SentenceCompletion 0.872 -0.140
## WordClassification 0.277 0.505 0.104
## WordMeaning 0.846 -0.108
## Addition -0.334 1.012
## CountingDots 0.206 -0.200 0.722 0.185
## ArithmeticProblems 0.197 0.500 0.139
## WordRecognition -0.126 0.127 -0.103 0.657
## NumberRecognition 0.568
## FigureRecognition 0.399 -0.142 -0.207 0.562
## ObjectNumber -0.108 0.107 0.613
## StraightCurvedCapitals 0.542 0.247 0.618
## Code 0.112 0.288 0.486 0.424
## NumberFigure 0.255 -0.230 0.211 0.413
## FigureWord 0.187 0.347
## Deduction 0.404 0.169 0.117 -0.203
## NumericalPuzzles 0.393 0.368
## ProblemReasoning 0.381 0.188 0.169
##
## Factor1 Factor2 Factor3 Factor4 Factor5
## SS loadings 3.529 3.311 2.367 2.109 0.762
## Proportion Var 0.147 0.138 0.099 0.088 0.032
## Cumulative Var 0.147 0.285 0.384 0.471 0.503