no. 3.] PSYCHOLOGICAL EXAMINING IN THE UNITED STATES ARMY. 649 



7? 

 In this form -^ is simply the ratio of two determinants, and the coefficients in the equations 



are in a more elemental form and resemble more closely the partial coefficients of correlation. 1 

 Hence, they tell a simpler story about the interdependence of the tests than they do after 

 each has been multiplied by the ratio of the standard deviations. A single glance at one of 

 these equations tells immediately the extent to which the test named in the left-hand member 

 of the equation is dependent on the various tests on the right-hand side. 



4 X = 1.33 +0.5644, 



4, = 2.73 + 0.461 A, 

 4, = 3.31 +0.1874, 

 4, = 1 .28 + 0.5054, + 0.0794, 

 4,= 1.55 + 0.4154 3 + 0.0744, 

 4, = 1.31 + 0.4264 2 - 0.0284 3 + 0.0794, 



4, = 2.99 + 0.2244,-0.10l4 3 + 0.0664 4 + 0.0444 5 + 0.1264 6 + 0.0354 7 + 0.0054, 

 a,= 0.290a,- 0.129a 3 + 0.262a 4 + 0.106a s + 0.183a 6 + 0.129a 7 + 0.018a, 



42 = 2.30 + 0.9464! 

 = 2.88 + 0.7554 3 

 = 4.24 + 0.2754, 



= 1.29 + 0.5784, + 0.4894 3 

 = 1.62 + 0.4894, + 0.3554 3 + 0.0824, 



= 2.74 + 0.2554, + 0.2144 3 + 0.0434 4 + 0.0494 5 + 0.2764, + 0.0284 7 - - 0.0154, 

 a 2 = 0.174a, + 0.211a 3 + 0.189a 4 + 0.092a 5 + 0.307a 6 + 0.080a 7 --0.040a g 



4 3 = 2.05 + 0.7554, 

 = 0.69 + 0.7364 2 

 = 3.27 + 0.4804, 

 = 3.77 + 0.2064, 



= 0.53 + 0.1244, + 0.6664 2 

 = 2.32 + 0.1864, + 0. 1814 2 + 0.2394 5 

 = 1.92 - 0.0354, + 0.3874 2 + 0.1384, 

 = 1.78 - 0.0234, + 0.4334 2 - 0.0464 + 0.1334, 

 = 2.05-0.0444, + 0.3574 2 + 0.1324 5 -0.0164 6 + 0.0834 8 

 = 3.08-0.1264, + 0.2654, + 0.1134 4 + 0.0524 5 -0.0564 6 + 0.03l4 7 + 0.0884 8 

 a 3 = - 0.098a, + 0.269a 2 + 0.351a 4 + 0.099a 3 - 0.063a, + 0.089a 7 + 0.242a, 



4 4 = -9.74 + 2.8184, 

 = - 12.37 + 2.4274 2 

 = -9.63 + 2.5004 3 

 = -5.70 + 1.8684, 

 = -5.91 + 1.004, 

 = - 13.86 + 1. 124, + 1.804 2 

 = - 13.52 + 1.424, + 1.844, 

 = -9.22 + 1.004, + 0.7884, 

 = - 12.68 + 1.354 2 + 0.6904, 

 = - 14.61 + 0.9404, + 0.8444 2 + 1.434 3 

 = -13.66 + 1.024, + 1.624 2 + 0.2724, 

 = -9.27 + 0.5614, + 0.8944 2 + 0.8344 5 



= - 10.55 + 0.5094, + 0.4794 2 + 0.6814 3 - 0.1574, + 0.1294 7 + 0.5084, 

 = _ 9.39 + 0.4824, + 0.4444 2 + 0.4274, + 0.3304 5 - 0.0874, + 0.41 74, 

 = - 10.12 + 0.4514, + 0.4184 2 + 0.6194, + 0.2834 5 - 0.1294 6 + 0.0704 7 + 0.4274, 

 a 4 = 0.114a, + 0.136a 2 + 0.199a 3 + 0.172a 5 -0.047a 6 + 0.066a 7 + 0.377a 8 



> All that is needed to convert these into partial coefficients of correlation is to multiply each one by its appropriate -J-^- See the formulffi 

 at the end of this section. 



121435°— 21 42 



