STATISTICAL METHODS IN PROTOZOOLOGY 45] 



Mean of jr = iiia; = 13. + o.oi = 13.01 

 Mean of 3; = uiy = S — 0.5 = 7.5 



— = -'^ = 0.4.^ 



N 100 ^^ 



VlX . Vxy = 0.005 



Difference =z 0.435 



Oa; . Oy = 0.8228 



Zxy 



, _JV 1^_ 0.435 __„o. 



(x — ntx) ^= r —(y — niy) 



Oy 



;r— 13.01 = 0.7132(3' — 7.5) 

 X = 7.6610 + 071327 



(y — ^%) = ^ — ('t' — i^x) 



Oy 



y — 7-5 = 0.3919 (.r— 13-01) 



3; = 2.4014 + o.39i9.r 



Ox.y = Ox V I-r^ = 0.8942 



Oy.x = Oy V l-r^ = 0.6629 



Having determined the constants and equations that arise in the 

 case of simple correlation, it would be well to look at the meaning 

 of these constants. 



The terms m^; = 13.01 and Wy = 7.5 indicate that the mean 

 length and breadth of the trophozoites are respectively 13.01 and 

 7.5 microns. 



The terms Ox = 1.05 and Oy ^= .78 measure in microns the varia- 

 bility of trophozoites as to length and breadth. 



The equation 



X = o.6769y + 7.94 



is used to determine the mean length of trophozoites that would 

 be expected in trophozoites of specific breadth. For example, in 

 considering a group of trophozoites all of breadth 8 microns, we 

 would substitute 8 for y in the above equation and determine the 

 value of X. This value, x = 13.07, states that the mean length of 



