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Factor Analysis

This page shows an example of a factor 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 factor analysis

Factor analysis is a method of data reduction. It does this by seeking underlying unobservable (latent) variables that are reflected in the observed variables (manifest variables). There are many different methods that can be used to conduct a factor analysis (such as principal axis factor, maximum likelihood, generalized least squares, unweighted least squares), There are also many different types of rotations that can be done after the initial extraction of factors, including orthogonal rotations, such as varimax and equimax, which impose the restriction that the factors cannot be correlated, and oblique rotations, such as promax, which allow the factors to be correlated with one another. You also need to determine the number of factors that you want to extract. Given the number of factor analytic techniques and options, it is not surprising that different analysts could reach very different results analyzing the same data set. However, all analysts are looking for simple structure. Simple structure is pattern of results such that each variable loads highly onto one and only one factor.

Factor analysis is a technique that requires a large sample size. Factor 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.

For the example below, we are going to do a rather "plain vanilla" factor
analysis. We will use iterated principal axis factor with three factors as our
method of extraction, a varimax rotation, and for comparison, we will also show
the promax oblique solution. The determination of the number of factors to
extract should be guided by theory, but also informed by running the analysis
extracting different numbers of factors and seeing which number of factors
yields the most interpretable results. We have used the **priors = smc**
option on the **proc factor** statement so that the squared multiple
correlation is used on the diagonal of the correlation matrix. (If this
option is not used, 1's are on the diagonal, and you will do a principal
components analysis instead of a principal axis factor analysis.)

In this example we have included many options, including the original correlation matrix, the scree plot and the eigenvectors. 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 principal components analysis that parallels this analysis. For general information regarding the similarities and differences between principal components analysis and factor analysis, see Tabachnick and Fidell, for example.

proc factor data = "d:\m255_sas" nfactors = 3 corr scree ev rotate = varimax method = prinit priors = smc; 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 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 factor (in other words, make its own
factor). This is not helpful, as the whole point of the analysis is to reduce
the number of items (variables).

Initial Factor Method: Iterated Principal Factor Analysis Prior Communality Estimates: SMC^{a}ITEM13 ITEM14 ITEM15 ITEM16 ITEM17 ITEM18 0.56418325 0.55109842 0.53781427 0.44669710 0.58542518 0.57168198 ITEM19 ITEM20 ITEM21 ITEM22 ITEM23 ITEM24 0.45593942 0.32641074 0.51564224 0.39697338 0.66171378 0.52583313 Preliminary Eigenvalues: Total = 6.13941289 Average = 0.51161774

Eigenvalue^{b}Difference^{c}Proportion^{d}Cumulative1 5.77616022 5.05422468 0.9408 0.9408 2 0.72193554 0.46721447 0.1176 1.0584 3 0.25472107 0.17543468 0.0415 1.0999 4 0.07928639 0.08287783 0.0129 1.1128 5 -.00359143 0.02084644 -0.0006 1.1122 6 -.02443788 0.04141429 -0.0040 1.1083 7 -.06585217 0.00923826 -0.0107 1.0975 8 -.07509043 0.02834695 -0.0122 1.0853 9 -.10343738 0.01757618 -0.0168 1.0685 10 -.12101355 0.02261532 -0.0197 1.0487 11 -.14362888 0.01200974 -0.0234 1.0254 12 -.15563862 -0.0254 1.0000^{e}

a. **Prior Communality Estimates: SMC** - This gives the
communality estimates prior to the rotation. The communalities (also known
as h^{2}) are the estimates of the variance of the factors, as opposed
to the variance of the variable which includes measurement error.

b. **Eigenvalue** - This is the initial eigenvalue. An eigenvalue is
the variance of the factor. Because this is an unrotated solution, the
first factor will account for the most variance, the second will account for the
second highest amount of variance, and so on. Some of the eigenvalues are
negative because the matrix is not of full rank. This means that there are
probably only four dimensions (corresponding to the four factors whose
eigenvalues are greater than zero). Although it is strange to have a
negative variance, this happens because the factor analysis is only analyzing
the common variance, which is less than the total variance. If we were
doing a principal components analysis, we would have had 1's on the diagonal,
which means that all of the variance is being analyzed (which is another way of
saying that we are assuming that we have no measurement error), and we would not
have negative eigenvalues. In general, it is not uncommon to have negative
eigenvalues.

c. **Difference** - This column gives the difference between the
eigenvalues. For example, 5.05 = 5.77 - 0.72. 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, 0.9408 = 5.77/6.139.

e. **Cumulative** - This is the sum of the proportion column. For
example, 1.0584 = 0.9408 + 0.1176.

3 factors will be retained by the NFACTOR criterion. Initial Factor Method: Iterated Principal Factor Analysis Scree Plot of Eigenvalues | 6 + | 1 | | | | 5 + | | | | | 4 + | | E | i | g | e 3 + n | v | a | l | u | e 2 + s | | | | | 1 + | | 2 | | 3 | 0 + 4 5 6 7 8 | 9 0 1 2 | | | | -1 + ----+------+------+------+------+------+------+------+------+------+------+------+------+---- 0 1 2 3 4 5 6 7 8 9 10 11 12 Number

The scree plot graphs the eigenvalue against the factor number. You can see these values in the first two columns of the table immediately above. From the third factor on, you can see that the line is almost flat, meaning the each successive factor is accounting for smaller and smaller amounts of the total variance.

Initial Factor Method: Iterated Principal Factor Analysis IterationChange^{f}^{g}Communalities^{h}1 0.0722 0.63235 0.60163 0.58315 0.47076 0.62245 0.64391 0.52673 0.36802 0.55072 0.44262 0.73027 0.58020 2 0.0314 0.65638 0.61511 0.59176 0.47107 0.62531 0.66684 0.55310 0.37241 0.55236 0.44807 0.76168 0.60660 3 0.0152 0.66649 0.61878 0.59279 0.46942 0.62437 0.67484 0.56471 0.37121 0.55092 0.44706 0.77683 0.61976 4 0.0075 0.67126 0.61963 0.59244 0.46846 0.62365 0.67765 0.57040 0.36997 0.54996 0.44578 0.78429 0.62641 5 0.0037 0.67367 0.61966 0.59202 0.46805 0.62329 0.67856 0.57338 0.36925 0.54949 0.44498 0.78797 0.62979 6 0.0018 0.67494 0.61950 0.59174 0.46789 0.62314 0.67877 0.57500 0.36887 0.54927 0.44456 0.78979 0.63153 7 0.0009 0.67562 0.61934 0.59156 0.46783 0.62308 0.67875 0.57591 0.36868 0.54917 0.44434 0.79068 0.63243 Convergence criterion satisfied.

f. **Iteration** - This column lists the number of the iteration. In
this analysis, seven iterations were required before the criteria was met.

g. **Change** - When the change becomes smaller than the criterion,
the iterating process stops. The numbers in this column are the largest absolute
difference between iterations. For example, the difference between the
first and the second iteration for item23 is 0.0314 = 0.73027 - 0.76168. The difference given for the first iteration is the difference
between the values at the first iteration and the squared multiple correlations
(sometimes called iteration 0).

h. **Communalities** - These are the communality estimates at each
iteration. For each iteration, the communality for each variable is
listed. For example, 0.63235 is the communality for the first variable.

Eigenvalues of the Reduced Correlation Matrix: Total = 7.01500876 Average = 0.58458406 Eigenvalue^{i}Difference^{j}Proportion^{k}Cumulative^{l}1 5.85107872 5.04474488 0.8341 0.8341 2 0.80633384 0.44633935 0.1149 0.9490 3 0.35999449 0.22853697 0.0513 1.0003 4 0.13145752 0.07654351 0.0187 1.0191 5 0.05491400 0.02332205 0.0078 1.0269 6 0.03159195 0.03030953 0.0045 1.0314 7 0.00128242 0.00617263 0.0002 1.0316 8 -.00489021 0.01439730 -0.0007 1.0309 9 -.01928750 0.02693109 -0.0027 1.0281 10 -.04621859 0.01408519 -0.0066 1.0216 11 -.06030378 0.03064032 -0.0086 1.0130 12 -.09094410 -0.0130 1.0000 Initial Factor Method: Iterated Principal Factor Analysis Eigenvectors^{m}1 2 3 ITEM13 INSTRUC WELL PREPARED 0.29486 -0.44338 0.15269 ITEM14 INSTRUC SCHOLARLY GRASP 0.29074 -0.37797 0.16283 ITEM15 INSTRUCTOR CONFIDENCE 0.29819 -0.27308 0.17609 ITEM16 INSTRUCTOR FOCUS LECTURES 0.26782 -0.21061 0.18546 ITEM17 INSTRUCTOR USES CLEAR RELEVANT EXAMPLES 0.32375 -0.08174 0.11086 ITEM18 INSTRUCTOR SENSITIVE TO STUDENTS 0.30573 0.38422 0.18861 ITEM19 INSTRUCTOR ALLOWS ME TO ASK QUESTIONS 0.25481 0.46205 0.25759 ITEM20 INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS 0.22744 0.26655 0.15574 ITEM21 INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING 0.30252 0.13020 0.00062 ITEM22 I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION 0.25337 0.29080 -0.03839 ITEM23 COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS 0.33865 -0.02903 -0.57488 ITEM24 COMPARED TO OTHER COURSES THIS COURSE WAS 0.28729 0.02042 -0.64369

i. **Eigenvalue** - This is the eigenvalue obtained after the
principal axis factoring but before the varimax rotation. An eigenvalue is
the variance of the factor. Because this is an unrotated solution, the
first factor will account for the most variance, the second will account for the
second highest amount of variance, and so on. Some of the eigenvalues are
negative because the matrix is not of full rank. This means that there are
probably only four dimensions (corresponding to the four factors whose
eigenvalues are greater than zero). Although it is strange to have a
negative variance, this happens because the factor analysis is only analyzing
the common variance, which is less than the total variance. If we were
doing a principal components analysis, we would have had 1's on the diagonal,
which means that all of the variance is being analyzed (which is another way of
saying that we are assuming that we have no measurement error), and we would not
have negative eigenvalues. In general, it is not uncommon to have negative
eigenvalues.

j. **Difference** - This column gives the difference between the
eigenvalues. For example, 5.0447 = 5.85107 - 0.8633. This column
allows you to see how quickly the eigenvalues are decreasing.

k. **Proportion** - This is the proportion of the total variance
that each factor accounts for. For example, 0.8341 = 5.85107/7.015.

l. **Cumulative** - This is the sum of the proportion column.
For example, 0.9490 = 0.8341 + 0.1149.

m. **Eigenvectors** - Eigenvectors are linear combinations of the
original variables. They tell you about the strength of the relationship
between the original variables and the (latent) factors.

Factor Pattern^{n}Factor1 Factor2 Factor3 ITEM13 INSTRUC WELL PREPARED 0.71324 -0.39814 0.09162 ITEM14 INSTRUC SCHOLARLY GRASP 0.70328 -0.33941 0.09770 ITEM15 INSTRUCTOR CONFIDENCE 0.72130 -0.24522 0.10565 ITEM16 INSTRUCTOR FOCUS LECTURES 0.64783 -0.18912 0.11128 ITEM17 INSTRUCTOR USES CLEAR RELEVANT EXAMPLES 0.78311 -0.07340 0.06652 ITEM18 INSTRUCTOR SENSITIVE TO STUDENTS 0.73953 0.34501 0.11316 ITEM19 INSTRUCTOR ALLOWS ME TO ASK QUESTIONS 0.61635 0.41490 0.15455 ITEM20 INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS 0.55015 0.23935 0.09344 ITEM21 INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING 0.73178 0.11691 0.00037 ITEM22 I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION 0.61288 0.26113 -0.02304 ITEM23 COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS 0.81916 -0.02607 -0.34493 ITEM24 COMPARED TO OTHER COURSES THIS COURSE WAS 0.69493 0.01834 -0.38621

n. **Factor Pattern** - This table contains the unrotated factor
loadings, which are the correlations between the variable and the factor.
Because these are correlations, possible values range from -1 to +1.

Variance Explained by Each Factor Factor1 Factor2 Factor3 5.8510787 0.8063338 0.3599945 Final Communality Estimates^{o}: Total = 7.017407^{p}ITEM13 ITEM14 ITEM15 ITEM16 ITEM17 ITEM18 0.67562309 0.61934326 0.59156382 0.46783384 0.62307645 0.67874757 ITEM19 ITEM20 ITEM21 ITEM22 ITEM23 ITEM24 0.57591368 0.36868496 0.54916770 0.44434233 0.79068338 0.63242696

o. **Final Communality Estimates** - This is the proportion of each
variable's variance that can be explained by the factors (e.g., the underlying
latent continua). The values here indicate the proportion of each
variable's variance that can be explained by the retained factors prior to the
rotation. Variables with high values are well represented in the common factor
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.

p. **Total** - 7.017407 = 5.8510787 + 0.8063338 +
0.3599945

Rotation Method: Varimax Orthogonal Transformation Matrix^{q}1 2 3 1 0.65843 0.61225 0.43773 2 -0.68417 0.72927 0.00910 3 0.31366 0.30547 -0.89906

q. **Orthogonal Transformation Matrix** - This is the matrix by
which you multiply the unrotated factor matrix to get the rotated factor matrix

Rotated Factor Pattern^{r}Factor1^{s}Factor2^{s}Factor3^{s}ITEM13 INSTRUC WELL PREPARED 0.77075 0.17432 0.22622 ITEM14 INSTRUC SCHOLARLY GRASP 0.72592 0.21291 0.21693 ITEM15 INSTRUCTOR CONFIDENCE 0.67583 0.29506 0.21852 ITEM16 INSTRUCTOR FOCUS LECTURES 0.59084 0.29271 0.18181 ITEM17 INSTRUCTOR USES CLEAR RELEVANT EXAMPLES 0.58671 0.44625 0.28233 ITEM18 INSTRUCTOR SENSITIVE TO STUDENTS 0.28638 0.73896 0.22512 ITEM19 INSTRUCTOR ALLOWS ME TO ASK QUESTIONS 0.17044 0.72715 0.13462 ITEM20 INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS 0.22779 0.53993 0.15899 ITEM21 INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING 0.40195 0.53341 0.32106 ITEM22 I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION 0.21766 0.55864 0.29137 ITEM23 COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS 0.44901 0.37716 0.66845 ITEM24 COMPARED TO OTHER COURSES THIS COURSE WAS 0.32388 0.32087 0.65159

r. **Rotated Factor Pattern** - This table contains the rotated
factor loadings, which are the correlations between the variable and the
factor. Because these are correlations, possible values range from -1 to +1.

s. **Factor** - These columns are the rotated factors that have been
extracted. These are the factors that analysts are most interested in and try
to name. For example, the first factor might be called "instructor competence"
because items like "instructor well prepare" and "instructor competence" load
highly on it. The second factor might be called "relating to students" because
items like "instructor is sensitive to students" and "instructor allows me to
ask questions" load highly on it. The third factor has to do with comparisons
to other instructors and courses.

Variance Explained by Each Factor Factor1 Factor2 Factor3 2.9494952 2.6557251 1.4121868 Final Communality Estimates: Total = 7.017407^{t}^{u}ITEM13 ITEM14 ITEM15 ITEM16 ITEM17 ITEM18 0.67562309 0.61934326 0.59156382 0.46783384 0.62307645 0.67874757 ITEM19 ITEM20 ITEM21 ITEM22 ITEM23 ITEM24 0.57591368 0.36868496 0.54916770 0.44434233 0.79068338 0.63242696

t. **Final Communality Estimates** - This is the proportion of each
variable's variance that can be explained by the factors (e.g., the underlying
latent continua). The values here indicate the proportion of each
variable's variance that can be explained by the retained factors after the
rotation. Variables with high values are well represented in the common
factor 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.

u. **Total** - 7.017407 = 2.9494952 + 2.6557251
+ 1.4121868

The partial output below shows the solution using a promax rotation. As you can see with an oblique rotation, such as a promax rotation, the factors are permitted to be correlated with one another. With an orthogonal rotation, such as the varimax shown above, the factors are not permitted to be correlated (they are orthogonal to one another). Oblique rotations, such as promax, produce both factor pattern and factor structure matrices. The factor pattern matrix gives the linear combination of the variables that make up the factors. The factor structure matrix presents the correlations between the variables and the factors. To completely interpret an oblique rotation one needs to take into account both the factor pattern and the factor structure matrices and the correlations among the factors.

Please note that with orthogonal rotations the factor pattern and the factor structure matrices are the equal.

Inter-Factor Correlations Factor1 Factor2 Factor3 Factor1 1.00000 0.59249 0.68096 Factor2 0.59249 1.00000 0.64863 Factor3 0.68096 0.64863 1.00000 Rotation Method: Promax (power = 3) Rotated Factor Pattern (Standardized Regression Coefficients) Factor1 Factor2 Factor3 ITEM13 INSTRUC WELL PREPARED 0.85071 -0.09207 0.03379 ITEM14 INSTRUC SCHOLARLY GRASP 0.78599 -0.02646 0.02406 ITEM15 INSTRUCTOR CONFIDENCE 0.69724 0.09144 0.01977 ITEM16 INSTRUCTOR FOCUS LECTURES 0.60443 0.12786 -0.00552 ITEM17 INSTRUCTOR USES CLEAR RELEVANT EXAMPLES 0.50870 0.28245 0.09868 ITEM18 INSTRUCTOR SENSITIVE TO STUDENTS 0.06335 0.76328 0.03145 ITEM19 INSTRUCTOR ALLOWS ME TO ASK QUESTIONS -0.04152 0.81872 -0.05898 ITEM20 INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS 0.07314 0.55467 0.00917 ITEM21 INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING 0.22482 0.42982 0.18931 ITEM22 I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION -0.00866 0.52669 0.19811 ITEM23 COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS 0.16276 0.07474 0.71794 ITEM24 COMPARED TO OTHER COURSES THIS COURSE WAS 0.02282 0.04596 0.7487 Rotated Factor Structure (Correlations) Factor1 Factor2 Factor3 ITEM13 INSTRUC WELL PREPARED 0.81917 0.43388 0.55337 ITEM14 INSTRUC SCHOLARLY GRASP 0.78670 0.45484 0.54213 ITEM15 INSTRUCTOR CONFIDENCE 0.76488 0.51738 0.55388 ITEM16 INSTRUCTOR FOCUS LECTURES 0.67643 0.48240 0.48901 ITEM17 INSTRUCTOR USES CLEAR RELEVANT EXAMPLES 0.74325 0.64786 0.62829 ITEM18 INSTRUCTOR SENSITIVE TO STUDENTS 0.53700 0.82121 0.56968 ITEM19 INSTRUCTOR ALLOWS ME TO ASK QUESTIONS 0.40340 0.75586 0.44379 ITEM20 INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS 0.40803 0.60396 0.41876 ITEM21 INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING 0.60841 0.68582 0.62121 ITEM22 I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION 0.43831 0.65006 0.53384 ITEM23 COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS 0.69593 0.63685 0.87725 ITEM24 COMPARED TO OTHER COURSES THIS COURSE WAS 0.55993 0.54515 0.79411

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