### SAS Annotated Output Principal Components Analysis

This page shows an example of a principal components analysis with footnotes explaining the output.  The data used in this example were collected by Professor James Sidanius, who has generously shared them with us.  You can download the data set here.

Overview:  The "what" and "why" of principal components analysis

Principal components analysis is a method of data reduction.  Suppose that you have a dozen variables that are correlated.  You might use principal components analysis to reduce your 12 measures to a few principal components.  In this example, you may be most interested in obtaining the component scores (which are variables that are added to your data set) and/or to look at the dimensionality of the data.  For example, if two components are extracted and those two components accounted for 68% of the total variance, then we would say that two dimensions in the component space account for 68% of the variance.  Unlike factor analysis, principal components analysis is not usually used to identify underlying latent variables.  Hence, the loadings onto the components are not interpreted as factors in a factor analysis would be.  Principal components analysis, like factor analysis, can be preformed on raw data, as shown in this example, or on a correlation or a covariance matrix.  If raw data is used, the procedure will create the original correlation matrix or covariance matrix, as specified by the user.  If the correlation matrix is used, the variables are standardized and the total variance will equal the number of variables used in the analysis (because each standardized variable has a variance equal to 1).  If the covariance matrix is used, the variables will remain in their original metric.  However, one must take care to use variables whose variances and scales are similar.  Unlike factor analysis, which analyzes the common variance, the original matrix in a principal components analysis analyzes the total variance.  Also, principal components analysis assumes that each original measure is collected without measurement error.

Principal components analysis is a technique that requires a large sample size.  Principal components analysis is based on the correlation matrix of the variables involved, and correlations usually need a large sample size before they stabilize.  Tabachnick and Fidell (2001, page 588) cite Comrey and Lee's (1992) advise regarding sample size: 50 cases is very poor, 100 is poor, 200 is fair, 300 is good, 500 is very good, and 1000 or more is excellent.  As a rule of thumb, a bare minimum of 10 observations per variable is necessary to avoid computational difficulties.

In this example we have included many options, including the original and reproduced correlation matrix and the scree plot.  While you may not wish to use all of these options, we have included them here to aid in the explanation of the analysis.  We have also created a page of annotated output for a factor analysis that parallels this analysis.  For general information regarding the similarities and differences between principal components analysis and factor analysis, see Tabachnick and Fidell (2001), for example.

proc factor data = "d:\m255_sas" corr scree residuals method = principal;
var item13 item14 item15 item16 item17 item18 item19 item20 item21 item22 item23 item24 ;
run;

* the results from the proc factor above and the proc princomp below are identical;
proc princomp data = "d:\m255_sas";
var item13 item14 item15 item16 item17 item18 item19 item20 item21 item22 item23 item24 ;
run;

The FACTOR Procedure

Correlations

ITEM13       ITEM14       ITEM15

ITEM13   INSTRUC WELL PREPARED                                   1.00000      0.66146      0.59999
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.66146      1.00000      0.63460
ITEM15   INSTRUCTOR CONFIDENCE                                   0.59999      0.63460      1.00000
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.56626      0.50003      0.50535
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.57687      0.55150      0.58664
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.40898      0.43311      0.45707
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.28632      0.32041      0.35869
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.30418      0.31481      0.35568
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.47553      0.44896      0.50904
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.33255      0.33313      0.36884
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.56399      0.56461      0.58233
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.45360      0.44281      0.43481

Correlations

ITEM16       ITEM17       ITEM18

ITEM13   INSTRUC WELL PREPARED                                   0.56626      0.57687      0.40898
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.50003      0.55150      0.43311
ITEM15   INSTRUCTOR CONFIDENCE                                   0.50535      0.58664      0.45707
ITEM16   INSTRUCTOR FOCUS LECTURES                               1.00000      0.58649      0.40479
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.58649      1.00000      0.55474
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.40479      0.55474      1.00000
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.33540      0.44930      0.62660
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.31676      0.41682      0.52055
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.45245      0.59526      0.55417
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.36255      0.44976      0.53609
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.45880      0.61302      0.56950
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.42967      0.52058      0.47382

Correlations

ITEM19       ITEM20       ITEM21

ITEM13   INSTRUC WELL PREPARED                                   0.28632      0.30418      0.47553
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.32041      0.31481      0.44896
ITEM15   INSTRUCTOR CONFIDENCE                                   0.35869      0.35568      0.50904
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.33540      0.31676      0.45245
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.44930      0.41682      0.59526
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.62660      0.52055      0.55417
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   1.00000      0.44647      0.49921
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.44647      1.00000      0.42479
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.49921      0.42479      1.00000
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.48404      0.38297      0.50651
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.44401      0.40962      0.59751
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.37383      0.35722      0.49977

The FACTOR Procedure

Correlations

ITEM22       ITEM23       ITEM24

ITEM13   INSTRUC WELL PREPARED                                   0.33255      0.56399      0.45360
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.33313      0.56461      0.44281
ITEM15   INSTRUCTOR CONFIDENCE                                   0.36884      0.58233      0.43481
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.36255      0.45880      0.42967
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.44976      0.61302      0.52058
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.53609      0.56950      0.47382
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.48404      0.44401      0.37383
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.38297      0.40962      0.35722
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.50651      0.59751      0.49977
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      1.00000      0.49317      0.44440
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.49317      1.00000      0.70464
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.44440      0.70464      1.00000

The table above was included in the output because we included the corr option on the proc factor statement.  This table gives the correlations between the original variables (which are specified on the var statement).  Before conducting a principal components analysis, you want to check the correlations between the variables.  If any of the correlations are too high (say above .9), you may need to remove one of the variables from the analysis, as the two variables seem to be measuring the same thing.  Another alternative would be to combine the variables in some way (perhaps by taking the average).  If the correlations are too low, say below .1, then one or more of the variables might load only onto one principal component (in other words, make its own principal component).  This is not helpful, as the whole point of the analysis is to reduce the number of items (variables).

The FACTOR Procedure
Initial Factor Method: Principal Components

Prior Communality Estimates: ONE

Eigenvalues of the Correlation Matrix: Total = 12  Average = 1

Eigenvalue    Difference    Proportion    Cumulative

1    6.24914661    5.01966832        0.5208        0.5208
2    1.22947829    0.51048923        0.1025        0.6232
3    0.71898906    0.10585957        0.0599        0.6831
4    0.61312949    0.05196458        0.0511        0.7342
5    0.56116491    0.05817383        0.0468        0.7810
6    0.50299107    0.03172750        0.0419        0.8229
7    0.47126357    0.08244834        0.0393        0.8622
8    0.38881523    0.02091149        0.0324        0.8946
9    0.36790373    0.03970330        0.0307        0.9252
10    0.32820043    0.01082277        0.0274        0.9526
11    0.31737767    0.06583773        0.0264        0.9790
12    0.25153994                      0.0210        1.0000

2 factors will be retained by the MINEIGEN criterion.

a.  Total and Average - The total of the eigenvalues is the sum of the values in the column labeled Eigenvalues.  It will always equal the number of variables that were used in the principal components analysis.  This is because each variable is assumed to be measured without error, and hence all of the variance is included in the analysis.  The average eigenvalue will always be one because the total will always sum to the number of variables used, and the average is found by dividing the total by the number of variables used.

b.  Eigenvalue - Eigenvalues are the variances of the principal components.  Because we conducted our principal components analysis on the correlation matrix, the variables are standardized, which means that the each variable has a variance of 1, and the total variance is equal to the number of variables used in the analysis, in this case, 12.

c.  Difference - This column gives the difference between the eigenvalues.  For example, 5.02 = 6.25 - 1.23.  This column allows you to see how quickly the eigenvalues are decreasing.

d.  Proportion - This is the proportion of the total variance that each factor accounts for.  For example, 0.5208 = 6.25/12.

e.  Cumulative - This is the sum of the proportion column.  For example, 0.6232 = 0.5208 + 0.1025.

f.  Mineigen criterion - The mineigen (minimum eigenvalue) criterion states that only components with eigenvalues above 1 should be retained.  In this example, only the first two components have eigenvalues greater than 1 (6.25 and 1.23), so these two should be retained.  Note that this criterion should be used only with principal components analysis and not factor analysis.  Components with an eigenvalue of less than 1 account for less variance than did the original variable (which had a variance of 1), and so are of little use.  Hence, you can see that the point of principal components analysis is to redistribute the variance in the correlation matrix (using the method of eigenvalue decomposition) to redistribute the variance to first components extracted.

The FACTOR Procedure
Initial Factor Method: Principal Components

Scree Plot of Eigenvalues
|
7 +
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6 +
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5 +
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E   |
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g   |
e 4 +
n   |
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e 3 +
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|                         3      4
|                                       5      6      7
|                                                            8      9      0      1      2
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0 +
-----+------+------+------+------+------+------+------+------+------+------+------+------+----
0      1      2      3      4      5      6      7      8      9     10     11     12

Number

The scree plot graphs the eigenvalue against the component number.  You can see these values in the first two columns of the table immediately above.  From the third component on, you can see that the line (pretend that the numbers are connected by a line) is almost flat, meaning the each successive component is accounting for smaller and smaller amounts of the total variance.  In general, we are interested in keeping only those principal components whose eigenvalues are greater than 1.  Components with an eigenvalue of less than 1 account for less variance than did the original variable (which had a variance of 1), and so are of little use.  Hence, you can see that the point of principal components analysis is to redistribute the variance in the correlation matrix (using the method of eigenvalue decomposition) to redistribute the variance to first components extracted.

The FACTOR Procedure
Initial Factor Method: Principal Components

Factor Pattern

Factor1         Factor2

ITEM13      INSTRUC WELL PREPARED                                      0.72729        -0.44919
ITEM14      INSTRUC SCHOLARLY GRASP                                    0.72378        -0.40766
ITEM15      INSTRUCTOR CONFIDENCE                                      0.74622        -0.30813
ITEM16      INSTRUCTOR FOCUS LECTURES                                  0.68511        -0.28137
ITEM17      INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                    0.80647        -0.10525
ITEM18      INSTRUCTOR SENSITIVE TO STUDENTS                           0.75512         0.36593
ITEM19      INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                      0.64098         0.49700
ITEM20      INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS         0.59269         0.37792
ITEM21      INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING                 0.76335         0.13454
ITEM22      I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION         0.65138         0.36448
ITEM23      COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS          0.81914        -0.04029
ITEM24      COMPARED TO OTHER COURSES THIS COURSE WAS                  0.71371         0.00467

This table contains component loadings, which are the correlations between the variable and the component.  Because these are correlations, possible values range from -1 to +1.  As you can see by the mineigen note above, two components were extracted (the two components that had an eigenvalue greater than 1).  You usually do not try to interpret the components the way that you would factors that have been extracted from a factor analysis.  Rather, most people are interested in the component scores, which are used for data reduction (as opposed to factor analysis where you are looking for underlying latent continua).

Variance Explained by Each Factor

Factor1         Factor2

6.2491466       1.2294783

Final Communality Estimates: Total = 7.478625

ITEM13          ITEM14          ITEM15          ITEM16          ITEM17          ITEM18

0.73071411      0.69004215      0.65179276      0.54854615      0.66147090      0.70412023

ITEM19          ITEM20          ITEM21          ITEM22          ITEM23          ITEM24

0.65786784      0.49410612      0.60081090      0.55713785      0.67261205      0.50940384

g.  Final Communality Estimates - This is the proportion of each variable's variance that can be explained by the components (e.g., the underlying latent continua).?????????  Variables with high values are well represented in the common component space, while variables with low values are not well represented.  (In this example, we don't have any particularly low values.)  They are the reproduced variances from the factors that you have extracted.  You can find these values on the diagonal of the reproduced correlation matrix.

h.  Total -   7.478625 = 6.2491466 + 1.2294783

The FACTOR Procedure
Initial Factor Method: Principal Components

Residual Correlations With Uniqueness on the Diagonal

ITEM13       ITEM14       ITEM15

ITEM13   INSTRUC WELL PREPARED                                   0.26929     -0.04805     -0.08113
ITEM14   INSTRUC SCHOLARLY GRASP                                -0.04805      0.30996     -0.03111
ITEM15   INSTRUCTOR CONFIDENCE                                  -0.08113     -0.03111      0.34821
ITEM16   INSTRUCTOR FOCUS LECTURES                              -0.05840     -0.11055     -0.09260
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                -0.05695     -0.07511     -0.04760
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.02416      0.03574      0.00633
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.04339      0.05909      0.03352
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.04288      0.03989      0.02984
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.01922     -0.04869     -0.01914
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.02253      0.01026     -0.00492
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.04986     -0.04469     -0.04134
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.06338     -0.07186     -0.09634

Residual Correlations With Uniqueness on the Diagonal

ITEM16       ITEM17       ITEM18

ITEM13   INSTRUC WELL PREPARED                                  -0.05840     -0.05695      0.02416
ITEM14   INSTRUC SCHOLARLY GRASP                                -0.11055     -0.07511      0.03574
ITEM15   INSTRUCTOR CONFIDENCE                                  -0.09260     -0.04760      0.00633
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.45145      0.00436     -0.00959
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.00436      0.33853     -0.01573
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                       -0.00959     -0.01573      0.29588
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.03610     -0.01532     -0.03929
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.01703     -0.02139     -0.06530
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.03268     -0.00620     -0.07149
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.01884     -0.03719     -0.08915
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.11374     -0.05183     -0.03431
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.05799     -0.05451     -0.06683

Residual Correlations With Uniqueness on the Diagonal

ITEM19       ITEM20       ITEM21

ITEM13   INSTRUC WELL PREPARED                                   0.04339      0.04288     -0.01922
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.05909      0.03989     -0.04869
ITEM15   INSTRUCTOR CONFIDENCE                                   0.03352      0.02984     -0.01914
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.03610      0.01703     -0.03268
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                -0.01532     -0.02139     -0.00620
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                       -0.03929     -0.06530     -0.07149
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.34213     -0.12126     -0.05695
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS     -0.12126      0.50589     -0.07849
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.05695     -0.07849      0.39919
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION     -0.11463     -0.14084     -0.03976
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.06102     -0.06065     -0.02237
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.08596     -0.06755     -0.04568

The FACTOR Procedure
Initial Factor Method: Principal Components

Residual Correlations With Uniqueness on the Diagonal

ITEM22       ITEM23       ITEM24

ITEM13   INSTRUC WELL PREPARED                                   0.02253     -0.04986     -0.06338
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.01026     -0.04469     -0.07186
ITEM15   INSTRUCTOR CONFIDENCE                                  -0.00492     -0.04134     -0.09634
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.01884     -0.11374     -0.05799
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                -0.03719     -0.05183     -0.05451
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                       -0.08915     -0.03431     -0.06683
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                  -0.11463     -0.06102     -0.08596
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS     -0.14084     -0.06065     -0.06755
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.03976     -0.02237     -0.04568
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.44286     -0.02571     -0.02220
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.02571      0.32739      0.12020
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.02220      0.12020      0.49060

The reproduced correlation matrix is the correlation matrix based on the extracted components.  You want the values in the reproduced matrix to be as close to the values in the original correlation matrix as possible.  This means that you want the residual matrix, which contains the differences between the original and the reproduced matrix, to be close to zero.  If the reproduced matrix is very similar to the original correlation matrix, then you know that the components that were extracted accounted for a great deal of the variance in the original correlation matrix, and these few components do a good job of representing the original data.

               Root Mean Square Off-Diagonal Residuals: Overall = 0.05960677

ITEM13          ITEM14          ITEM15          ITEM16          ITEM17          ITEM18

0.04975192      0.05810347      0.05378868      0.06298003      0.04176665      0.04931537

Root Mean Square Off-Diagonal Residuals: Overall = 0.05960677

ITEM19          ITEM20          ITEM21          ITEM22          ITEM23          ITEM24

0.06860859      0.07278550      0.04562254      0.06469198      0.06466964      0.07276449

Partial Correlations Controlling Factors

ITEM13       ITEM14       ITEM15

ITEM13   INSTRUC WELL PREPARED                                   1.00000     -0.16630     -0.26495
ITEM14   INSTRUC SCHOLARLY GRASP                                -0.16630      1.00000     -0.09471
ITEM15   INSTRUCTOR CONFIDENCE                                  -0.26495     -0.09471      1.00000
ITEM16   INSTRUCTOR FOCUS LECTURES                              -0.16749     -0.29552     -0.23355
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                -0.18861     -0.23187     -0.13865
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.08559      0.11802      0.01973
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.14294      0.18146      0.09710
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.11616      0.10074      0.07111
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.05861     -0.13843     -0.05134
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.06525      0.02770     -0.01254
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.16792     -0.14030     -0.12245
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.17436     -0.18427     -0.23308

The FACTOR Procedure
Initial Factor Method: Principal Components

Partial Correlations Controlling Factors

ITEM16       ITEM17       ITEM18

ITEM13   INSTRUC WELL PREPARED                                  -0.16749     -0.18861      0.08559
ITEM14   INSTRUC SCHOLARLY GRASP                                -0.29552     -0.23187      0.11802
ITEM15   INSTRUCTOR CONFIDENCE                                  -0.23355     -0.13865      0.01973
ITEM16   INSTRUCTOR FOCUS LECTURES                               1.00000      0.01115     -0.02623
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.01115      1.00000     -0.04970
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                       -0.02623     -0.04970      1.00000
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.09186     -0.04501     -0.12350
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.03564     -0.05169     -0.16878
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.07698     -0.01687     -0.20802
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.04214     -0.09606     -0.24629
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.29584     -0.15569     -0.11024
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.12321     -0.13377     -0.17541

Partial Correlations Controlling Factors

ITEM19       ITEM20       ITEM21

ITEM13   INSTRUC WELL PREPARED                                   0.14294      0.11616     -0.05861
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.18146      0.10074     -0.13843
ITEM15   INSTRUCTOR CONFIDENCE                                   0.09710      0.07111     -0.05134
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.09186      0.03564     -0.07698
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                -0.04501     -0.05169     -0.01687
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                       -0.12350     -0.16878     -0.20802
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   1.00000     -0.29146     -0.15411
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS     -0.29146      1.00000     -0.17465
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.15411     -0.17465      1.00000
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION     -0.29449     -0.29756     -0.09457
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.18231     -0.14904     -0.06187
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.20982     -0.13560     -0.10321

Partial Correlations Controlling Factors

ITEM22       ITEM23       ITEM24

ITEM13   INSTRUC WELL PREPARED                                   0.06525     -0.16792     -0.17436
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.02770     -0.14030     -0.18427
ITEM15   INSTRUCTOR CONFIDENCE                                  -0.01254     -0.12245     -0.23308
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.04214     -0.29584     -0.12321
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                -0.09606     -0.15569     -0.13377
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                       -0.24629     -0.11024     -0.17541
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                  -0.29449     -0.18231     -0.20982
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS     -0.29756     -0.14904     -0.13560
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING             -0.09457     -0.06187     -0.10321
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      1.00000     -0.06751     -0.04762
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS      -0.06751      1.00000      0.29993
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS              -0.04762      0.29993      1.00000

The FACTOR Procedure
Initial Factor Method: Principal Components

Root Mean Square Off-Diagonal Partials: Overall = 0.15731128

ITEM13          ITEM14          ITEM15          ITEM16          ITEM17          ITEM18

0.15638661      0.16741220      0.14768643      0.16260912      0.12339790      0.13993481

Root Mean Square Off-Diagonal Partials: Overall = 0.15731128

ITEM19          ITEM20          ITEM21          ITEM22          ITEM23          ITEM24

0.18120479      0.16671240      0.11770355      0.15605275      0.17596042      0.17781950

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