STATISTICAL ?yIETHODS IN PROTOZOOLOGY 



457 



With the value of y^, we go to Pearson's Table for Statisticians 

 and Biomctricians, page 26, and we look in the column headed 

 n' = 6, this being the number of classes for which we are making 

 our comparison. Within this column we interpolate for a value of 

 P to correspond to a value of ;^- = 3.138. For this value, we find 

 0.679. The interpretation of this probability is as follows: If there 

 were no difference in the number of spines of parent and off- 

 spring and we repeated the above sampling process many 

 times, we would expect to get samples as different as or more 

 different than the ones that did appear, 68 times in 100. Thus, 

 we may conclude that in the present case there is no reason 

 for assuming that parent and offspring differ as to the number 

 of their spines. If P had been small, we would have concluded 

 that the difference was significant. In general, it is dangerous 

 to assume that differences are significant unless P is as small 

 as o.oi. 



The '/^ test has an entirely different method of computation 

 when we wish to compare a sample with a theoretical distribution. 

 As an illustration of this, consider the distribution of length of 

 trophozoites in comparison with the theoretical distribution as 

 given in the section on frequency distribution. The computation 

 for /- in this case is as follows : 



5.0482 



With this value of y^, a value of P is found as in the preceding 

 example. This value of P is .283, and indicates that in sampling 

 from a normal distribution we would get as large discrepancies as 

 did occur in this sample, 28 times in 100. Thus we may state that 

 the distribution is essentially normal. : " 



