PRINCIPAL COMPONENT ANALYSIS Program: PCA - Analysis Output Title: PCA Example Data One (scores as person per row) Data read from file: PCA_DataOne.txt Program execution initiated at 10:59:21 on 17-Jul-2011 Program executed at 10:59:34 on 17-Jul-2011 Correlation matrix used ALL EIGENVALUES Component Unordered Eigenvalue Proportion Cumulative Difference index as % percentage 1 2 2.85686 40.812288 40.812288 1.623438 2 3 1.233423 17.620321 58.432609 0.097921 3 5 1.135501 16.221445 74.654054 0.475923 4 4 0.659578 9.42254 84.076594 0.155805 5 6 0.503773 7.196758 91.273352 0.059223 6 7 0.444551 6.350722 97.624075 0.278236 7 1 0.166315 2.375926 100.0 EXTRACTED EIGENVALUES Greater than unity Greater than Monte Carlo Mean Greater than Monte Carlo Percentile Component Eigenvalue Proportion Cumulative Eigenvalue Proportion Cumulative Eigenvalue Proportion Cumulative as % percentage as % percentage as % percentage 1 2.85686 40.812288 40.812288 2.85686 40.812288 40.812288 2.85686 40.812288 40.812288 2 1.233423 17.620321 58.432609 3 1.135501 16.221445 74.654054 PARALLEL ANALYSIS Number of simulations = 200 Gaussian random deviates used Percentile value used = 95.0 % Component Data Proportion Cumulative Data Monte Carlo Monte Carlo Monte Carlo Eigenvalue as % percentage Eigenvalue Eigenvalue Eigenvalue Eigenvalue Percentile Mean Standard Deviation 1 2.85686 40.812288 40.812288 2.85686 2.274269 1.883991 0.130184 2 1.233423 17.620321 58.432609 1.233423 1.662948 1.464384 0.094973 3 1.135501 16.221445 74.654054 1.135501 1.357542 1.17731 0.087451 4 0.659578 9.42254 84.076594 0.659578 1.093148 0.931489 0.069145 5 0.503773 7.196758 91.273352 0.503773 0.847144 0.708693 0.052815 6 0.444551 6.350722 97.624075 0.444551 0.67517 0.512625 0.032981 7 0.166315 2.375926 100.0 0.166315 0.467959 0.32151 0.027427 CORRELATION MATRIX Original item indices in parenthesis item 2 (1) 3 (2) 5 (3) 4 (4) 6 (5) 7 (6) 1 (7) item 2 (1) 1.0 0.481491 -0.070094 0.205071 0.197667 0.561255 0.788254 3 (2) 0.481491 1.0 0.339464 0.318519 0.102776 0.355933 0.47796 5 (3) -0.070094 0.339464 1.0 0.128446 -0.019968 -0.038169 0.165316 4 (4) 0.205071 0.318519 0.128446 1.0 0.334525 0.178737 0.243441 6 (5) 0.197667 0.102776 -0.019968 0.334525 1.0 0.060363 0.184914 7 (6) 0.561255 0.355933 -0.038169 0.178737 0.060363 1.0 0.565669 1 (7) 0.788254 0.47796 0.165316 0.243441 0.184914 0.565669 1.0 PARTIAL CORRELATION MATRIX Original item indices in parenthesis item 2 (1) 3 (2) 5 (3) 4 (4) 6 (5) 7 (6) 1 (7) item 2 (1) 1.0 0.302923 -0.381958 -0.048027 0.087316 0.146408 0.680487 3 (2) 0.302923 1.0 0.388333 0.213415 -0.047993 0.110534 -0.012033 5 (3) -0.381958 0.388333 1.0 0.031335 -0.046387 -0.140556 0.337396 4 (4) -0.048027 0.213415 0.031335 1.0 0.316276 0.060773 0.053431 6 (5) 0.087316 -0.047993 -0.046387 0.316276 1.0 -0.096068 0.052117 7 (6) 0.146408 0.110534 -0.140556 0.060773 -0.096068 1.0 0.256924 1 (7) 0.680487 -0.012033 0.337396 0.053431 0.052117 0.256924 1.0 COVARIANCE MATRIX Original item indices in parenthesis item 2 (1) 3 (2) 5 (3) 4 (4) 6 (5) 7 (6) 1 (7) item 2 (1) 26.355731 2.08498 -0.367589 1.332016 0.393281 2.920949 12.398419 3 (2) 2.08498 0.711463 0.29249 0.339921 0.033597 0.304348 1.235178 5 (3) -0.367589 0.29249 1.043478 0.166008 -0.007905 -0.039526 0.517391 4 (4) 1.332016 0.339921 0.166008 1.600791 0.164032 0.229249 0.943676 6 (5) 0.393281 0.033597 -0.007905 0.164032 0.150198 0.023715 0.219565 7 (6) 2.920949 0.304348 -0.039526 0.229249 0.023715 1.027668 1.756917 1 (7) 12.398419 1.235178 0.517391 0.943676 0.219565 1.756917 9.386957 EIGENVECTORS Original component indices in parenthesis Vector corresponding to an ordered eigenvalues in each row component 2 (1) 3 (2) 5 (3) 4 (4) 6 (5) 7 (6) 1 (7) component 1 (2) 0.502317 0.422469 0.112724 0.27819 0.190779 0.420546 0.515603 2 (3) -0.299892 0.276879 0.672396 0.43715 0.243958 -0.335731 -0.133997 3 (5) 0.009741 -0.261496 -0.479898 0.41027 0.717001 -0.088434 -0.104837 4 (4) -0.155525 0.098872 -0.284619 0.688007 -0.550142 0.237898 -0.228961 5 (6) -0.252798 -0.613181 0.388592 0.073282 0.087063 0.62389 0.083128 6 (7) 0.301194 -0.514646 0.102427 0.288172 -0.282171 -0.504124 0.465968 7 (1) 0.691979 -0.160783 0.249744 0.037709 -0.011875 0.051284 -0.654789 LOADING FACTORS Original indices in parenthesis Loading factors corresponding to an ordered eigenvalues in each row component 2 (1) 3 (2) 5 (3) 4 (4) 6 (5) 7 (6) 1 (7) Eigenvalue Proportion Cumulative % factor 1 (2) 0.849029 0.714068 0.190528 0.470203 0.322459 0.710817 0.871484 2.85686 40.812288 40.812288 2 (3) -0.333059 0.3075 0.74676 0.485497 0.270939 -0.372862 -0.148816 1.233423 17.620321 58.432609 3 (5) 0.01038 -0.27865 -0.511379 0.437184 0.764035 -0.094235 -0.111714 1.135501 16.221445 74.654054 4 (4) -0.126309 0.080299 -0.231152 0.55876 -0.446795 0.193208 -0.185949 0.659578 9.42254 84.076594 5 (6) -0.179429 -0.435217 0.275811 0.052013 0.061795 0.442818 0.059002 0.503773 7.196758 91.273352 6 (7) 0.20082 -0.343138 0.068293 0.192138 -0.188137 -0.336123 0.310682 0.444551 6.350722 97.624075 7 (1) 0.282201 -0.06557 0.10185 0.015378 -0.004843 0.020915 -0.267034 0.166315 2.375926 100.0 ROTATED LOADING FACTORS NORMAL VARIMAX Varimax rotation for 3 extracted factors Rotated loading factors and eigenvalues scaled to ensure total 'rotated variance' matches unrotated variance for the extracted factors Original indices in parenthesis component 2 (1) 5 (2) 3 (3) 4 (4) 6 (5) 7 (6) 1 (7) Eigenvalue Proportion Cumulative % factor 1 (2) 0.898562 0.547614 -0.073019 0.149932 0.06166 0.807249 0.858022 2.526761 36.975093 36.975093 2 (5) 0.153716 0.17009 7.723591E-4 0.747188 0.859946 0.001416 0.148521 1.372418 20.083133 57.058226 3 (3) -0.029029 0.594377 0.922024 0.259149 -0.133521 -0.038908 0.189342 1.326604 19.412721 76.470947 Kaiser-Meyer-Olkin (KMO) statistic Overall KMO statistic = 0.658981 KMO values for each item 1 2 3 4 5 6 7 0.631435 0.728937 0.276732 0.700285 0.616917 0.85786 0.665516 Bartlett Sphericity Test Chi-Square = 43.688797 Probability value = 0.002565 Degrees of freedom = 21 Chi-Square value at the 5% significance level (p = 0.05) = 32.670573 Chi-Square value at the 10% significance level (p = 0.10) = 29.615089 DATA USED Number of items = 7 Number of persons = 23 Person item1 item2 item3 item4 item5 item6 item7 1 39.0 2.0 1.0 3.0 2.0 1.0 4.9 2 35.0 2.0 -1.0 2.0 2.0 -1.0 -0.3 3 35.0 3.0 1.0 3.0 2.0 1.0 -1.2 4 38.0 2.0 -1.0 2.0 1.0 -1.0 -1.9 5 40.0 3.0 -1.0 3.0 2.0 -1.0 2.7 6 43.0 5.0 1.0 6.0 2.0 1.0 3.2 7 46.0 3.0 1.0 3.0 2.0 1.0 3.6 8 35.0 2.0 1.0 6.0 2.0 -1.0 -1.0 9 35.0 2.0 -1.0 4.0 2.0 -1.0 -2.1 10 32.0 2.0 -1.0 3.0 2.0 -1.0 -1.9 11 40.0 3.0 1.0 3.0 2.0 1.0 4.5 12 41.0 2.0 -1.0 4.0 2.0 1.0 2.2 13 30.0 2.0 -1.0 3.0 1.0 1.0 -2.6 14 39.0 3.0 1.0 3.0 2.0 -1.0 3.5 15 33.0 2.0 -1.0 3.0 2.0 1.0 0.8 16 44.0 2.0 -1.0 5.0 2.0 1.0 4.4 17 32.0 1.0 1.0 2.0 1.0 -1.0 -1.5 18 43.0 4.0 1.0 4.0 1.0 1.0 8.3 19 30.0 2.0 1.0 6.0 2.0 -1.0 1.4 20 45.0 2.0 -1.0 3.0 2.0 1.0 6.5 21 31.0 2.0 1.0 3.0 2.0 -1.0 -0.4 22 44.0 2.0 -1.0 5.0 2.0 1.0 3.7 23 42.0 3.0 -1.0 5.0 2.0 1.0 4.2