# The Intellectuals and McCarthy: The Radical Specter

By Michael Paul Rogin | Go to book overview

APPENDIX B
FACTOR ANALYSIS

Factor analysis aims at discovering underlying relationships that exist in any table of numbers. Consider Table B.1:

TABLE B.1
HYPOTHETICAL DATA TABLE
 2 4 6 8 10 12 1 2 3 4 5 6 1 1 1 1 1 1

It is clear that the first two rows are proportional to each other; multiply the second row by the constant 2 and you reproduce the first row. We can say that this matrix of three rows can be reduced to two rows that are independent of each other--that is to say, no operation that can be performed on either of the two independent rows can make them identical. Factor analysis aims at reducing all the rows of a data table to the number that are independent of each other. By performing mathematical operations on the rows of a factor matrix, it is possible to reproduce the original data matrix to a given degree of approximation.1

There is a mathematically precise method of calculating optimal values for a given number of rows (or factors) from the original data table. This is known as the principal axis solution. The first principal axis is that row of numbers that accounts for the largest sum of squares of the entries in each row of the original matrix. Once the correlations corresponding to the principal axis have been subtracted from the

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