24 STATISTICAL METHODS. 



also the skewness (p. 30) should be less than twice the value 

 .67449 /- 



To determine the closeness of fit of a theoreti- 

 cal polygon to the observed polygon. Find for 

 each class the difference (<^) between the theoretical value (y) 

 and the observed frequency (/). Divide the square of this 

 difference in each case by y. The square root of the sum of the 



/~d~ 2 

 quotients is the index of closeness of fit (/). Or, A= 4/ I 



a 



The probability (P:l) that the observed distribution is truly 

 represented by the theoretical polygon may be calculated from 

 the following formula, to use which the number of classes 

 (A) must be odd or must be made odd by the addition of a 

 class with frequency. 



__ 

 2 2.42.4.6 



4ZL_\ 

 .4.6...,l-3/' 



This is the method of Pearson, 1900 & . 



To determine the probability of a given dis- 

 tribution being normal. Having found, in units of the 

 standard deviation, the deviation (7) of the inner limiting 

 value (L) of each class from the average, look up the 

 corresponding class-index a from Table IV. Or, better, find a 

 directly for each class by dividing the half of the total num- 

 ber of variates minus all those lying beyond the inner limit- 

 ing value of the class in question by the half of the total 



I */ 



number of variates; or, in a formula, -y -; where JT Y / means 



?n 



add all the frequencies from the median value to ^, and n 

 is the number of variates. Next find for each class the sum 

 of A-}- a%. This should equal L. The difference is the 

 actual discrepancy. The probable discrepancy should next be 

 calculated for all but the extreme values. It is calculated 

 by use of the formula 



0.6745, 



