read the literature in metallurgy. Geometry, and economics will recognize that, in the initial study, all of the
information is contained in five of the original 11 variables – namely length, width, height, density, and cost per
pound. The remaining six variables are merely built up from the five “underlying factors” by additions and
multiplications. Since a rather simple model will give a perfect explanation, it is difficult to get excited about a
factor analytic model which “explains” 90.7% of the total information.
The factor analysis was unable to uncover the basic dimensions. It determined that there were three rather
than five basic factors. And the interpretation of these factors was not easy. In fact, one suspects that, had the field
followed alone the lines advocated by Swift (by measuring intensity, shortness, and compactness), progress would
have been much slower! The Swift study could easily mislead other researchers.
As one other example of how the researchers could be misled we can take the following. Both volume and
surface area load heavily on Factor 1. We could go back to the original matrix and find that the correlation
coefficient between surface area and volume is .969. We conclude that, allowing for some measurement error, these
variables are really measuring the same thing and we are just as well off if we know either one of them as when we
know both. This statement is, of course, a good approximation to this set of data. But if we tried to go beyond our
data it is easy to see where the reasoning breaks down. That is. one can construct a very thin right-angled
parallelepiped with surface area equal to that of a cube but with volume much smaller.
If Mr. Swift had not followed his original “rules” he might have done a little better. Let us say that he
dropped the rule that the eigenvalues must be greater than 1.0. The fourth factor has an eigenvalue of .55; the fifth is
.27 and the sixth is .09. He then rotates four factors, then five, etc. In this case the rotation of five factors showed
that he had gone too far as none of the variables achieved a high loading (.70) on the fifth factor.
The four factor rotation is interesting. however. Thus is shown in Table 2.