No. 498] 



NOTES AND LITERATURE 



121 



answer usually given is that 2 per cent, is to lie expected, with a 

 probable error ot a certain amount. In calculating this prob- 

 able error in the ordinary way it is assumed that the distribu- 

 tion of chances is given by the normal or (iaussian curve of 

 errors. Pearson shows that this is not true except (1) when the 

 first sample is indefinitely large in proportion to the second, and 

 (2) when the characteristic does not occur in either a very large 

 or very small percentage of the population. He then proceeds to 

 develop general formula' from which one may determine first 

 the average expectancy for the second sample and its true prob- 

 able error, and second the frequency of future samples having 

 varying derives of the characteristic under consideration. These 

 methods are fully illustrated with numerical examples. The 

 usefulness of the methods for biological work may be indicated 

 by an example. Suppose that in a sample of 200 tadpoles, 106 are 

 males and 94 females. Suppose, further, that in a second sam- 

 ple of 300 collected later in the season the proportion is 171 males 

 to 129 females. Is it to be concluded that between the collections 

 some factor has come into operation tending to the greater pro- 

 hibited in the second sample what might be regarded as a rea- 



vvherein the sex. determining factors had not changed since the 

 first sample was collected? The paper under discussion furnishes 

 the methods whereby questions of this sort may be definitely 

 answered. 



ods of determining the degr< f correlation between variates. 



The methods are adapted for use in cases where for one reason 



method of finding a correlation coefficient. It is neither possible 

 nor desirable to enter upon any detailed discussion of the mathe- 

 matical features of these new methods here. Three new methods 

 are given. The first, or "difference method" of determining 

 correlation, furnishes a very simple and tolerably accurate way 

 of deducing a correlation coefficient from a symmetrical (e. g., 

 homotypic) correlation table. The other two methods are con- 



