Real Statistics Data Analysis Tool: The Real Statistics Resource Pack contains the Factor Analysis data analysis tool, which automates most of the Factor Analysis capabilities described elsewhere in this website.
To access this data analysis tool, first press Ctrl-m and then choose the Multivariate Analyses option from the resulting menu. From the dialog box that appears select the Factor Analysis option and click on the OK button. The dialog box in 1 will then appear.
If you click on the Help button the following dialog box will appear.
As seen in Figure 1, you are presented with a choice between using Principal Component extraction or Principal Axis extraction. You can choose to use Varimax rotation or not. You can also choose to specify the number of factors to use in the model (# of Factors); if this field is left blank then the Kaiser criterion is used, namely that all factors whose eigenvalue is 1 or greater are retained.
Principal Component Extraction
If you choose the Principal Component extraction option then the following output will appear (all the data refers to Example 1 of Factor Extraction):
In order to display the rotated factor matrix shown in range B114:E122, the VARIMAX supplemental array function is used. This function is provided in the Real Statistics Resource Pack.
VARIMAX(R1, iter, prec) = the result of rotating the square matrix defined by range R1 using the Varimax algorithm, where iter is the maximum number of iterations (default 100) and prec is the value that is considered to be sufficiently close to zero (default 0.00001).
In Figure 7, range B114:E122 contains the formula =VARIMAX(M100:P108).
Principal Axis Extraction
If you choose the Principal Axis extraction method then the output is similar to that described above. In fact, the output starts out identically as described in Figure 3 and 4 (except that the title is Factor Analysis – Principal Axis Extraction).
As described in Principal Axis Extraction, the Real Statistics software next calculates the initial communalities and revised communalities (using the ExtractCommunalities supplemental function) as described in Figure 11.
From this point on the data analysis tool calculates its results exactly as in Principal Component extraction except that the revised correlation matrix (range M96:104 in Figure 11) is used as the correlation matrix.