/*-------------------------------------------------------------|
 |          Spearman's (1904) Two-Factor Theory                |
 |                                                             |
 |Spearman used this data to argue for a 'two-factor theory'   |
 |of ability in which all correlations among variables could be|
 |accounted for by a single general factor ('ability') plus one|
 |unique factor for each test.                                 |
 |-------------------------------------------------------------*/
title "Spearman's five variables:  Harman, Pp 116,391-392";
 
data spear5 (TYPE=CORR);
    input _TYPE_ $ 1-8 _NAME_ $ 9-16
          test1 17-20 test2 22-25 test3 27-30
          test4 32-35 test5 37-40;
    label test1='Mathematical judgement'
          test2='Controlled association'
          test3='Literary interpretation'
          test4='Selective judgement'
          test5='Spelling';
    datalines;
CORR    test1	1.00  .    .	.	 .
CORR    test2	.485 1.00  .	.	 .
CORR    test3	.400 .397 1.00  .	 .
CORR    test4	.397 .397 .335 1.00  .
CORR    test5	.295 .247 .275 .195 1.00
N               100  100  100  100  100
proc print;
/* Note: _TYPE_ = N obs. is necessary for proper Chisq test */
proc factor data=spear5
     method=ml         /* use maximum likelihood      */
     residuals         /* print residual correlations */
     nfact=1;          /* estimate one factor         */
title2 'Test of hypothesis of one general factor';
run;