.65

.20

.4625

.70

.09

.4981

.60

30

.4500

.20

.60

.4000

.15

.55

.3250

-.25

.50

.3125

1.40

.80

2.2

23.33%

13.33%

36.66%

## Some Importantant Terminology

This is the correlation between a given test and a given factor. Like any correlation, it will range from -1.0 to +1.0, and it can be squared to determine the proportion of variability acounted for by this factor.

### Communality (common variance)

This is the overall proportion of variance attributable to the factors

(e.g., for Picture Completion, communality = .20*.02 + .60*.60 = .4000)

### Extracted variance (eigenvalue)

This is a measure of the amount of variance in all the tests that is accounted for by the factor (it is a sum of squares).

The eigenvalue is often converted to percentages:

(eigenvalue x 100)/number of tests

When a factor has a large eigenvalue, we assume this is because the factor represents some trait or characteristic common to the tests.

## Factor Rotation

In order to better interpret the factors, a procedure called rotation is often used.

Rotation involves re-distributing the tests’ commonalities so that a clearer pattern of loadings emerges. The aim is to find an arrangement in which tests load high on one factor and low on others.

The factors can be viewed as axes that define a space in which the tests are displayed. Rotation moves the factors until the most simple alignment with the tests is found. Rotation can be orthogonal or oblique: in the former the factors are kept "at right angles" to each other (i.e. they remain uncorrelated); in the latter they are allowed to become correlated.

Although the factor loadings of each subtest are changed by rotation, their communality and the factors’ eigenvalues are unchanged:

 Subtest Loadings on Factor 1' Loadings on Factor 2' communality Information .68 .01 .4625 Vocabulary .70 .09 .4981 Similarities .66 .12 .4500 Picture Completion .05 .63 .4000 Block Design .01 .57 .3250 Object Assembly .10 .55 .3125 Extracted variance (eigenvalues) 1.40 .80 2.2 Percentage variance 23.33% 13.33% 36.66%

Notice that the subtests have loadings on the rotated factors that tend to be higher or lower than they were on the unrotated factors. The rotated factors "line up" better with the tests.