PRINCIPAL COMPONENT ANALYSIS Program: PCA - Analysis Output Title: PCA Example Data Two (scores as person per row) Data read from file: PCA_DataTwo.txt Program execution initiated at 10:59:59 on 17-Jul-2011 Program executed at 11:00:11 on 17-Jul-2011 Correlation matrix used ALL EIGENVALUES Component Unordered Eigenvalue Proportion Cumulative Difference index as % percentage 1 2 2.830931 40.44187 40.44187 1.655328 2 3 1.175603 16.794325 57.236195 0.129467 3 4 1.046136 14.944795 72.18099 0.308176 4 5 0.737959 10.542277 82.723266 0.186491 5 6 0.551468 7.878115 90.601382 0.124907 6 7 0.426561 6.093733 96.695114 0.195219 7 1 0.231342 3.304886 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 2.830931 40.44187 40.44187 2.830931 40.44187 40.44187 2.830931 40.44187 40.44187 2 1.175603 16.794325 57.236195 3 1.046136 14.944795 72.18099 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 2.830931 40.44187 40.44187 2.830931 2.224112 1.877647 0.148322 2 1.175603 16.794325 57.236195 1.175603 1.66956 1.44806 0.11283 3 1.046136 14.944795 72.18099 1.046136 1.349857 1.171406 0.091911 4 0.737959 10.542277 82.723266 0.737959 1.073274 0.934356 0.051124 5 0.551468 7.878115 90.601382 0.551468 0.88686 0.726811 0.044438 6 0.426561 6.093733 96.695114 0.426561 0.66099 0.51582 0.040479 7 0.231342 3.304886 100.0 0.231342 0.45351 0.3259 0.005872 CORRELATION MATRIX Original item indices in parenthesis item 2 (1) 3 (2) 4 (3) 5 (4) 6 (5) 7 (6) 1 (7) item 2 (1) 1.0 0.488511 0.034654 0.265369 0.233631 0.407826 0.727304 3 (2) 0.488511 1.0 0.353753 0.335013 0.126665 0.340935 0.469801 4 (3) 0.034654 0.353753 1.0 0.051373 -0.023473 -0.036648 0.128127 5 (4) 0.265369 0.335013 0.051373 1.0 0.341638 0.287994 0.240071 6 (5) 0.233631 0.126665 -0.023473 0.341638 1.0 0.101077 0.227553 7 (6) 0.407826 0.340935 -0.036648 0.287994 0.101077 1.0 0.544652 1 (7) 0.727304 0.469801 0.128127 0.240071 0.227553 0.544652 1.0 PARTIAL CORRELATION MATRIX Original item indices in parenthesis item 2 (1) 3 (2) 4 (3) 5 (4) 6 (5) 7 (6) 1 (7) item 2 (1) 1.0 0.27045 -0.180714 0.049234 0.067505 -0.046417 0.600124 3 (2) 0.27045 1.0 0.382295 0.216666 -0.046177 0.127296 0.075487 4 (3) -0.180714 0.382295 1.0 -0.011778 -0.048952 -0.178848 0.150776 5 (4) 0.049234 0.216666 -0.011778 1.0 0.311904 0.184366 -0.069887 6 (5) 0.067505 -0.046177 -0.048952 0.311904 1.0 -0.094728 0.114146 7 (6) -0.046417 0.127296 -0.178848 0.184366 -0.094728 1.0 0.398095 1 (7) 0.600124 0.075487 0.150776 -0.069887 0.114146 0.398095 1.0 COVARIANCE MATRIX Original item indices in parenthesis item 2 (1) 3 (2) 4 (3) 5 (4) 6 (5) 7 (6) 1 (7) item 2 (1) 25.952479 2.085838 0.175808 1.707363 0.459053 1.971468 10.955269 3 (2) 2.085838 0.702479 0.295267 0.354621 0.040947 0.271153 1.164256 4 (3) 0.175808 0.295267 0.991736 0.064613 -0.009016 -0.034632 0.377273 5 (4) 1.707363 0.354621 0.064613 1.595041 0.166416 0.34514 0.896488 6 (5) 0.459053 0.040947 -0.009016 0.166416 0.14876 0.036993 0.259504 7 (6) 1.971468 0.271153 -0.034632 0.34514 0.036993 0.900433 1.528139 1 (7) 10.955269 1.164256 0.377273 0.896488 0.259504 1.528139 8.7425 EIGENVECTORS Original component indices in parenthesis Vector corresponding to an ordered eigenvalues in each row component 2 (1) 3 (2) 4 (3) 5 (4) 6 (5) 7 (6) 1 (7) component 1 (2) 0.481143 0.43034 0.125376 0.323745 0.234056 0.397397 0.500073 2 (3) -0.055885 0.377323 0.775598 -0.220023 -0.423418 -0.158923 0.001521 3 (4) -0.231437 0.095196 0.337548 0.515572 0.597146 -0.352662 -0.27689 4 (5) 0.343992 -0.11807 0.085225 -0.601699 0.484674 -0.441136 0.262517 5 (6) -0.389039 -0.346323 0.37699 -0.260428 0.331132 0.633543 0.087979 6 (7) 0.246541 -0.715551 0.301618 0.383887 -0.251065 -0.1732 0.309564 7 (1) 0.617536 -0.132207 0.168618 -0.061083 0.041976 0.257825 -0.707652 LOADING FACTORS Original indices in parenthesis Loading factors corresponding to an ordered eigenvalues in each row component 2 (1) 3 (2) 4 (3) 5 (4) 6 (5) 7 (6) 1 (7) Eigenvalue Proportion Cumulative % factor 1 (2) 0.80954 0.724063 0.210949 0.544713 0.393808 0.668635 0.841392 2.830931 40.44187 40.44187 2 (3) -0.060593 0.409113 0.840944 -0.23856 -0.459092 -0.172313 0.00165 1.175603 16.794325 57.236195 3 (4) -0.236716 0.097367 0.345247 0.527331 0.610765 -0.360705 -0.283205 1.046136 14.944795 72.18099 4 (5) 0.295505 -0.101428 0.073212 -0.516887 0.416357 -0.378956 0.225514 0.737959 10.542277 82.723266 5 (6) -0.288904 -0.257183 0.279956 -0.193396 0.245901 0.470475 0.065334 0.551468 7.878115 90.601382 6 (7) 0.16102 -0.467339 0.196991 0.250723 -0.163974 -0.11312 0.202181 0.426561 6.093733 96.695114 7 (1) 0.297023 -0.063589 0.081102 -0.02938 0.02019 0.124009 -0.340367 0.231342 3.304886 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) 4 (2) 3 (3) 5 (4) 6 (5) 7 (6) 1 (7) Eigenvalue Proportion Cumulative % factor 1 (2) 0.820068 0.541903 -0.057363 0.219895 0.06486 0.770148 0.866188 2.36543 34.946806 34.946806 2 (4) 0.182124 0.191942 -0.027702 0.750946 0.854308 0.077295 0.130487 1.387542 20.499511 55.446317 3 (3) 0.096858 0.608785 0.931034 0.13938 -0.069542 -0.08815 0.14436 1.299698 19.201705 74.648022 Kaiser-Meyer-Olkin (KMO) statistic Overall KMO statistic = 0.682091 KMO values for each item 1 2 3 4 5 6 7 0.690544 0.740663 0.384219 0.704472 0.660628 0.727941 0.674767 Bartlett Sphericity Test Chi-Square = 37.052806 Probability value = 0.016601 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 38.045455 2.0 1.0 6.0 2.0 -1.0 -1.0 9 35.0 2.0 -1.0 3.636364 2.0 -1.0 -2.1 10 32.0 2.0 -1.0 3.0 2.0 0.238095 1.95 11 40.0 3.0 1.0 3.0 2.0 1.0 4.5 12 41.0 2.454546 -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 1.818182 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 -0.090909 6.0 2.0 0.238095 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