194 Appendix 



(ID; m — = or m — - 



Cy <Jy n <7x a ay ay n ax ay 



which is called r, or the Pearsonian Coefficient of Correlation, 



and it determines the tangent of the angle which the best 



fitting straight lines makes with the x axis, expressed in terms 



of the standard deviations of the two series. 



2 YY 

 Example: In table 17, ~~ is 246,210, ay is 1,220, and ax is 



249. ax ay is, therefore 303,500 and r = U6 > 210 = .811. 

 ' 303,500 



» PMJmiBLL EMUn; Willi lilt luiniulu r.C«-VV r thopvobablcerroj ' 



jtf jhr rn n ffi n i nn t , 111 1 i V V & x J U - \'~ m^ ±.141. Thk . 



rnpa^g tVint Mj\th akt , 1 1 ■ 1 1 r !Ji'/M<i tgrits " r ' 1 | " m hdata thguaaefficifin. t 



mi ^ht b ^ ^ fo p fh in %" ih i I iiiii , i fi TO ' 



Graphic Presentation. —The advantage of having the scale of 

 Diagram III laid out in units proportional to the two standard 

 deviations, i.e. of having the unit along the horizontal axis rep- 

 resent an increase of 100 in farms, and the unit along the 



100 X 1220 



vertical axis represent an increase of - 



249 

 in population is now apparent. For as r is the tangent of 

 the angle which the best fitting line makes the x axis, ex- 

 pressed in terms of the standard deviations, then, when the 

 scale is expressed in terms of the standard deviation, r has a 

 direct relationship to the tangent of the angle. Then the 

 straight line which is the linear representation of the coefficient 

 of relationship .811 is plotted by passing a line through the zero 

 point (located at the means of the systems) and the point 

 whose coordinates are 1, .811. (For this method of graphic 

 expression of correlation coefficients I am indebted to Mr. 

 Frank A. Ross, of the faculty of Political Science, Columbia 

 University.) This also explains why several correlation co- 

 efficients may be presented on the same system of coordinates 

 as in diagram II. In this diagram one unit on the x axis 

 represents, in turn, increases of 100 in farms, share tenants, 

 cash tenants, owners, and acres cultivated by laborer, while in 



each case the unit on the y axis is ?. In other 



ax 



words the units used are proportions instead of actual num- 

 bers and since they are proportions they may be legitimately 

 compared on the same scale, the real comparison being be- 

 tween the slopes of the 5 regression lines. 



