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Holzinger & Swineford 9 Ability Variables 1 Principal factor solution

     OBS    _NAME_    _TYPE_         X1         X2         X4         X6
       1     X1        CORR       1.000       .          .          .
       2     X2        CORR       0.318      1.000       .          .
       3     X4        CORR       0.436      0.419      1.000       .
       4     X6        CORR       0.335      0.234      0.323      1.000
       5     X7        CORR       0.304      0.157      0.283      0.722
       6     X9        CORR       0.326      0.195      0.350      0.714
       7     X10       CORR       0.116      0.057      0.056      0.203
       8     X12       CORR       0.314      0.145      0.229      0.095
       9     X13       CORR       0.489      0.239      0.361      0.309
      10               N        145.000    145.000    145.000    145.000
      11               MEAN      29.600     24.800     15.970      9.950
      12               STD        6.890      4.430      8.290      3.360
      13               RELI       0.756      0.568      0.937      0.750
     OBS         X7         X9        X10        X12        X13
       1       .          .          .          .          .
       2       .          .          .          .          .
       3       .          .          .          .          .
       4       .          .          .          .          .
       5      1.000       .          .          .          .
       6      0.685      1.000       .          .          .
       7      0.246      0.170      1.000       .          .
       8      0.181      0.113      0.585      1.000       .
       9      0.345      0.280      0.408      0.512      1.000
      10    145.000    145.000    145.000    145.000    145.000
      11     18.850     90.180     68.590    109.750    191.800
      12      4.630      7.920     23.700     20.920     36.910
      13      0.754      0.870      0.952      0.937      0.889

Holzinger & Swineford 9 Ability Variables 2 Principal factor solution

Initial Factor Method: Principal Factors

                     Prior Communality Estimates: SMC
                      X1        X2        X4        X6        X7
                0.368471  0.208053  0.341968  0.631033  0.596939

                      X9       X10       X12       X13
                0.583642  0.413615  0.472166  0.442670
                Eigenvalues of the Reduced Correlation Matrix:
                    Total = 4.05855691  Average = 0.45095077
                          1           2           3           4           5
   Eigenvalue        3.0733      1.0793      0.6202      0.0304     -0.0779
   Difference        1.9939      0.4592      0.5898      0.1082      0.0324
   Proportion        0.7572      0.2659      0.1528      0.0075     -0.0192
   Cumulative        0.7572      1.0232      1.1760      1.1835      1.1643

                          6           7           8           9
   Eigenvalue       -0.1103     -0.1490     -0.1755     -0.2320
   Difference        0.0386      0.0265      0.0565
   Proportion       -0.0272     -0.0367     -0.0432     -0.0572
   Cumulative        1.1371      1.1004      1.0572      1.0000
           2 factors will be retained by the PROPORTION criterion.

Holzinger & Swineford 9 Ability Variables 3 Principal factor solution

Initial Factor Method: Principal Factors
                          Scree Plot of Eigenvalues

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       ----+------+------+------+------+------+------+------+------+------+---
           0      1      2      3      4      5      6      7      8      9

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Holzinger & Swineford 9 Ability Variables 4 Principal factor solution

Initial Factor Method: Principal Factors

                                Factor Pattern
                        FACTOR1   FACTOR2

             X1           57 *      13       Visual Perception
             X2           37         4       Cubes
             X4           53 *       2       Lozenges
             X6           74 *     -39       Paragraph Comprehen
             X7           72 *     -31       Sentence Completion
             X9           71 *     -38       Word Meaning
             X10          41        44       Addition
             X12          46        59 *     Counting Dots
             X13          62 *      36       Straight-curved Caps
NOTE: Printed values are multiplied by 100 and rounded to the nearest
      integer.  Values greater than 0.480314 have been flagged by an '*'.

                      Variance explained by each factor
                                FACTOR1   FACTOR2
                               3.073280  1.079350

                Final Communality Estimates: Total = 4.152630

                      X1        X2        X4        X6        X7
                0.340931  0.139830  0.281143  0.691859  0.619334
                      X9       X10       X12       X13
                0.642764  0.360407  0.558927  0.517435

Holzinger & Swineford 9 Ability Variables 5 Principal factor solution

Rotation Method: Varimax

                       Orthogonal Transformation Matrix
                                       1         2

                             1      0.81762   0.57576
                             2     -0.57576   0.81762
                            Rotated Factor Pattern
                        FACTOR1   FACTOR2

             X1           39        43       Visual Perception
             X2           28        25       Cubes
             X4           42        32       Lozenges
             X6           83 *      11       Paragraph Comprehen
             X7           77 *      17       Sentence Completion
             X9           80 *      10       Word Meaning
             X10           8        59 *     Addition
             X12           3        75 *     Counting Dots
             X13          30        65 *     Straight-curved Caps
NOTE: Printed values are multiplied by 100 and rounded to the nearest
      integer.  Values greater than 0.480314 have been flagged by an '*'.

                      Variance explained by each factor
                                FACTOR1   FACTOR2
                               2.412285  1.740345

                Final Communality Estimates: Total = 4.152630

                      X1        X2        X4        X6        X7
                0.340931  0.139830  0.281143  0.691859  0.619334
                      X9       X10       X12       X13
                0.642764  0.360407  0.558927  0.517435

Holzinger & Swineford 9 Ability Variables 6 Maximum liklihood solution, k=2

Initial Factor Method: Maximum Likelihood

                     Prior Communality Estimates: SMC
                      X1        X2        X4        X6        X7
                0.368471  0.208053  0.341968  0.631033  0.596939

                      X9       X10       X12       X13
                0.583642  0.413615  0.472166  0.442670
      Preliminary Eigenvalues:  Total = 8.35308162  Average = 0.92812018
                          1           2           3           4           5
   Eigenvalue        6.5717      2.1601      0.9945      0.0464     -0.1550
   Difference        4.4116      1.1657      0.9481      0.2014      0.0787
   Proportion        0.7867      0.2586      0.1191      0.0056     -0.0186
   Cumulative        0.7867      1.0453      1.1644      1.1700      1.1514

                          6           7           8           9
   Eigenvalue       -0.2337     -0.2818     -0.3308     -0.4184
   Difference        0.0481      0.0490      0.0876
   Proportion       -0.0280     -0.0337     -0.0396     -0.0501
   Cumulative        1.1234      1.0897      1.0501      1.0000
             2 factors will be retained by the NFACTOR criterion.

  Iter Criterion    Ridge   Change   Communalities
    1    0.45507    0.000  0.22709   0.30206 0.11542 0.23431 0.75766 0.65405
                                     0.68683 0.29953 0.69926 0.54539

    2    0.44408    0.000  0.09778   0.29506 0.10314 0.22413 0.76216 0.67244
                                     0.67826 0.39731 0.66878 0.50244

    3    0.44153    0.000  0.05393   0.28226 0.10012 0.21674 0.76131 0.67341
                                     0.67909 0.38181 0.72271 0.48910

    4    0.44073    0.000  0.01789   0.27721 0.09773 0.21419 0.76200 0.67319
                                     0.67820 0.39970 0.73120 0.47697

    5    0.44048    0.000  0.01432   0.27354 0.09666 0.21224 0.76172 0.67340
                                     0.67804 0.39989 0.74552 0.47109

    6    0.44041    0.000  0.00421   0.27179 0.09595 0.21135 0.76186 0.67336
                                     0.67780 0.40356 0.74973 0.46738

    7    0.44039    0.000  0.00361   0.27078 0.09563 0.21082 0.76183 0.67341
                                     0.67773 0.40408 0.75334 0.46558

    8    0.44039    0.000  0.00132   0.27029 0.09544 0.21057 0.76186 0.67341
                                     0.67767 0.40488 0.75466 0.46457

Holzinger & Swineford 9 Ability Variables 7 Maximum liklihood solution, k=2

Initial Factor Method: Maximum Likelihood
    9    0.44039    0.000  0.00089   0.27003 0.09535 0.21043 0.76186 0.67342
                                     0.67765 0.40508 0.75555 0.46409

                       Convergence criterion satisfied.

       Significance tests based on 145 observations:
          Test of H0: No common factors.
               vs HA: At least one common factor.

          Chi-square = 483.448   df = 36   Prob>chi**2 = 0.0001

          Test of H0: 2 Factors are sufficient.
               vs HA: More factors are needed.

          Chi-square = 61.141   df = 19   Prob>chi**2 = 0.0001

       Chi-square without Bartlett's correction = 63.415857147
       Akaike's Information Criterion = 25.415857147
       Schwarz's Bayesian Criterion = -31.14208396
       Tucker and Lewis's Reliability Coefficient = 0.8215541861
                        Squared Canonical Correlations
                                FACTOR1   FACTOR2
                               0.897947  0.797742
           Eigenvalues of the Weighted Reduced Correlation Matrix:
                    Total = 12.7429834  Average = 1.41588704
                          1           2           3           4           5
   Eigenvalue        8.7988      3.9442      0.8646      0.0863      0.0291
   Difference        4.8546      3.0796      0.7782      0.0573      0.1312
   Proportion        0.6905      0.3095      0.0678      0.0068      0.0023
   Cumulative        0.6905      1.0000      1.0678      1.0746      1.0769

                          6           7           8           9
   Eigenvalue       -0.1022     -0.1534     -0.3404     -0.3839
   Difference        0.0513      0.1870      0.0435
   Proportion       -0.0080     -0.0120     -0.0267     -0.0301
   Cumulative        1.0689      1.0568      1.0301      1.0000

Holzinger & Swineford 9 Ability Variables 8 Maximum liklihood solution, k=2

Initial Factor Method: Maximum Likelihood

                                Factor Pattern
                        FACTOR1   FACTOR2

             X1           49 *      17       Visual Perception
             X2           30         6       Cubes
             X4           45         8       Lozenges
             X6           82 *     -31       Paragraph Comprehen
             X7           80 *     -20       Sentence Completion
             X9           77 *     -28       Word Meaning
             X10          40        50 *     Addition
             X12          41        77 *     Counting Dots
             X13          54 *      41       Straight-curved Caps
NOTE: Printed values are multiplied by 100 and rounded to the nearest
      integer.  Values greater than 0.489523 have been flagged by an '*'.

                      Variance explained by each factor
                                     FACTOR1   FACTOR2
                        Weighted    8.798797  3.944188
                        Unweighted  3.059945  1.253437
               Final Communality Estimates and Variable Weights
       Total Communality: Weighted = 12.742985   Unweighted = 4.313382
                            X1        X2        X4        X6        X7
        Communality   0.269931  0.095308  0.210380  0.761863  0.673416
        Weight        1.369918  1.105402  1.266520  4.199216  3.062007

                            X9       X10       X12       X13
        Communality   0.677641  0.405294  0.755584  0.463964
        Weight        3.102188  1.680901  4.090860  1.865972

Holzinger & Swineford 9 Ability Variables 9 Maximum liklihood solution, k=3

Initial Factor Method: Maximum Likelihood

                     Prior Communality Estimates: SMC
                      X1        X2        X4        X6        X7
                0.368471  0.208053  0.341968  0.631033  0.596939

                      X9       X10       X12       X13
                0.583642  0.413615  0.472166  0.442670
      Preliminary Eigenvalues:  Total = 8.35308162  Average = 0.92812018
                          1           2           3           4           5
   Eigenvalue        6.5717      2.1601      0.9945      0.0464     -0.1550
   Difference        4.4116      1.1657      0.9481      0.2014      0.0787
   Proportion        0.7867      0.2586      0.1191      0.0056     -0.0186
   Cumulative        0.7867      1.0453      1.1644      1.1700      1.1514

                          6           7           8           9
   Eigenvalue       -0.2337     -0.2818     -0.3308     -0.4184
   Difference        0.0481      0.0490      0.0876
   Proportion       -0.0280     -0.0337     -0.0396     -0.0501
   Cumulative        1.1234      1.0897      1.0501      1.0000
             3 factors will be retained by the NFACTOR criterion.

  Iter Criterion    Ridge   Change   Communalities
    1    0.06962    0.000  0.20697   0.46963 0.26591 0.49235 0.75568 0.70683
                                     0.67838 0.58904 0.67913 0.52759

    2    0.06913    0.000  0.01335   0.47637 0.26921 0.47900 0.75937 0.70294
                                     0.67715 0.60216 0.68357 0.52314

    3    0.06909    0.000  0.00401   0.47953 0.26520 0.47712 0.75992 0.70222
                                     0.67687 0.60473 0.68305 0.52402

    4    0.06909    0.000  0.00172   0.48081 0.26429 0.47540 0.76003 0.70199
                                     0.67686 0.60632 0.68217 0.52464

    5    0.06909    0.000  0.00071   0.48152 0.26370 0.47471 0.76006 0.70190
                                     0.67687 0.60693 0.68181 0.52494

                       Convergence criterion satisfied.

Holzinger & Swineford 9 Ability Variables 10 Maximum liklihood solution, k=3

Initial Factor Method: Maximum Likelihood

       Significance tests based on 145 observations:
          Test of H0: No common factors.
               vs HA: At least one common factor.

          Chi-square = 483.448   df = 36   Prob>chi**2 = 0.0001

          Test of H0: 3 Factors are sufficient.
               vs HA: More factors are needed.

          Chi-square = 9.545   df = 12   Prob>chi**2 = 0.6558

       Chi-square without Bartlett's correction = 9.9483002058
       Akaike's Information Criterion = -14.05169979
       Schwarz's Bayesian Criterion = -49.7725047
       Tucker and Lewis's Reliability Coefficient = 1.0164579945
                        Squared Canonical Correlations
                           FACTOR1   FACTOR2   FACTOR3
                          0.903641  0.785919  0.607902
           Eigenvalues of the Weighted Reduced Correlation Matrix:
                    Total = 14.5993195  Average = 1.62214661
                          1           2           3           4           5
   Eigenvalue        9.3778      3.6711      1.5504      0.2574      0.1292
   Difference        5.7067      2.1207      1.2930      0.1282      0.1396
   Proportion        0.6423      0.2515      0.1062      0.0176      0.0088
   Cumulative        0.6423      0.8938      1.0000      1.0176      1.0265

                          6           7           8           9
   Eigenvalue       -0.0105     -0.0460     -0.1358     -0.1944
   Difference        0.0355      0.0898      0.0586
   Proportion       -0.0007     -0.0032     -0.0093     -0.0133
   Cumulative        1.0258      1.0226      1.0133      1.0000

Holzinger & Swineford 9 Ability Variables 11 Maximum liklihood solution, k=3

Initial Factor Method: Maximum Likelihood

                                Factor Pattern
                   FACTOR1   FACTOR2   FACTOR3

        X1           51 *      18        43       Visual Perception
        X2           32         7        39       Cubes
        X4           48 *       8        49 *     Lozenges
        X6           81 *     -30        -8       Paragraph Comprehen
        X7           80 *     -21       -16       Sentence Completion
        X9           77 *     -28        -4       Word Meaning
        X10          40        55 *     -37       Addition
        X12          40        72 *      -6       Counting Dots
        X13          56 *      43        16       Straight-curved Caps
NOTE: Printed values are multiplied by 100 and rounded to the nearest
      integer.  Values greater than 0.437686 have been flagged by an '*'.

                      Variance explained by each factor
                                FACTOR1   FACTOR2   FACTOR3
                   Weighted    9.377808  3.671130  1.550383
                   Unweighted  3.119394  1.274658  0.778313
               Final Communality Estimates and Variable Weights
       Total Communality: Weighted = 14.599322   Unweighted = 5.172365
                            X1        X2        X4        X6        X7
        Communality   0.481645  0.263525  0.474592  0.760059  0.701883
        Weight        1.928724  1.358143  1.903696  4.167689  3.354550

                            X9       X10       X12       X13
        Communality   0.676866  0.606967  0.681812  0.525016
        Weight        3.094698  2.544051  3.142778  2.104990

Holzinger & Swineford 9 Ability Variables 12 Maximum liklihood solution, k=3

Rotation Method: Varimax

                       Orthogonal Transformation Matrix
                                  1         2         3

                        1      0.81846   0.37363   0.43649
                        2     -0.48734   0.85383   0.18294
                        3     -0.30433  -0.36245   0.88091
                            Rotated Factor Pattern
                   FACTOR1   FACTOR2   FACTOR3

        X1           20        19        64 *     Visual Perception
        X2           11         4        50 *     Cubes
        X4           21         7        65 *     Lozenges
        X6           84 *       7        23       Paragraph Comprehen
        X7           80 *      18        17       Sentence Completion
        X9           78 *       6        25       Word Meaning
        X10          17        76 *      -5       Addition
        X12          -1        79 *      26       Counting Dots
        X13          20        52 *      47 *     Straight-curved Caps
NOTE: Printed values are multiplied by 100 and rounded to the nearest
      integer.  Values greater than 0.437686 have been flagged by an '*'.

                      Variance explained by each factor
                                FACTOR1   FACTOR2   FACTOR3
                   Weighted    7.297477  4.189182  3.112663
                   Unweighted  2.117154  1.544175  1.511036
               Final Communality Estimates and Variable Weights
       Total Communality: Weighted = 14.599322   Unweighted = 5.172365
                            X1        X2        X4        X6        X7
        Communality   0.481645  0.263525  0.474592  0.760059  0.701883
        Weight        1.928724  1.358143  1.903696  4.167689  3.354550

                            X9       X10       X12       X13
        Communality   0.676866  0.606967  0.681812  0.525016
        Weight        3.094698  2.544051  3.142778  2.104990

Holzinger & Swineford 9 Ability Variables 13 Maximum liklihood solution, k=3 Variance decomposition for each test

                                         Common   Unique  Specific  Error
  Test Name                 Reliability Variance Variance Variance Variance
  X1   Visual Perception        0.756     0.482    0.518    0.275    0.244
  X2   Cubes                    0.568     0.264    0.736    0.304    0.432
  X4   Lozenges                 0.937     0.475    0.525    0.462    0.064
  X6   Paragraph Comprehen      0.750     0.760    0.240   -0.010    0.250
  X7   Sentence Completion      0.754     0.702    0.298    0.052    0.246
  X9   Word Meaning             0.870     0.677    0.323    0.193    0.130
  X10  Addition                 0.952     0.607    0.393    0.345    0.048
  X12  Counting Dots            0.937     0.682    0.318    0.256    0.063
  X13  Straight-curved Caps     0.889     0.525    0.475    0.364    0.111