456 



RESEARCH IN PROTOZOOLOGY 



no real difference between the number of spines in parent and off- 

 spring in the general universe. 



By the procedure above outlined, we may determine the signifi- 

 cance to be attached to differences between any two statistical 

 constants. 



CHI-SQUARE TEST 



In addition to questioning the significance of the difference be- 

 tween any two statistical constants, we often question significance 

 in a more general form. We consider the distributions of measure- 

 ments that we wish to compare and ask the general question as 

 to whether or not they are samples that might very probably have 

 come from the same distribution, the idea involved being that if 

 we find that it is quite probable that they might have arisen from 

 the same distribution we would attach no significance to any of the 

 differences that may exist between these distributions. If, on the 

 other hand, we find that they are samples that would be very 

 unlikely to come from the same universe, we will attach signifi- 

 cance to their dift"erences. To answer this question, a statistical 

 method called the Chi-square test has been developed. This method 

 depends upon the derivation of a general variation constant, ^", 

 and the relationship between this constant and the probability that 

 such differences as were observed might have arisen by sampling 

 alone. The use of this test may perhaps be made clear by an 

 example and we shall apply this test to see whether or not the 

 general distributions of parent and offspring of Difflugia corona 

 as to number of spines are significantly different. 



CHI-SQUARE TEST 

 NUMBER OF SPINES OF PARENT AND OFFSPRING OF DiMugia CoYOna 



Chi-square = x' = 69 X 69 X .0065916 = 3.13826 



