Path: Janda's Home Page > Workshop > Factor Analysis > Outline
Principal components analysis computes the underlying factor that accounts for the maximum variance held in common among a set of intercorrelated variables.
Then it computes a second uncorrelated (orthogonal) factor to account for the maximum remaining variance.
It proceeds to calculate separate, uncorrelated factors until all variance in the original matrix is exhausted.
--The number of factors extracted depends on the intercorrelations in the matrix.
--The lower the correlations, the less common variance, so more factors are needed to account for large proportions of the variance.
Two Principal Components Accounted for 98.5 Per Cent of Total Variance from Eight Rectangle Tests on One Hundred Cases

First Component
Second Component
(also "Latent Root")
Eigenvalue
5.96
1.93

Per Cent of Variance
74.4
24.1

Variable
Factor I
Factor II
1
Length
0.85*
-0.52
2
Width
0.63
0.76
3
10Length + e
0.86
-0.50
4
10Width +e
0.63
0.74
5
20L + 10Width + e
0.98
-0.18
6
20L + 20Width + e
0.99
0.08
7
10L + 20Width + e
0.93
0.37
8
40L + 10Width + e
0.94
-0.34
*This value (0.85), which is called the factor "loading," is the correlation of that variable (length) with the underlying factor.

We know (from constructing the data) that the only variance not accounted for by the first two factors is error variance due to the error term. Let's see a plot of this analysis.

Continue to page 5: A plot of the unrotated factors