cxxiv Tables for Statisticians and Biometricians [XXV 



Accordingly at the end of Table XXV we have placed the probability integral of 

 the normal curve with a standard deviation where n = 31, for comparison 



V71-3 



with that of the curve 



The result confirms the inference drawn from the value of $>, i.e. that the 

 normal curve will only give a rough approximation to the exact probability integral 

 at w = 31. At the top of the table we may be in error in two to three units in the 

 third place of decimals*. 



2. We will now describe the two tables here provided. 



Table XXV gives the value of 



where the argument x increases by '01. 



We need to know the relations between m and n, and x and x' , 



Curve (i). m\ lies between and 1, and the only values available in our table are 



x' z 



for n = 2 and 3, or wj = 0'5 and 0, while x is determined by # = 2 . 



ctj_ 



Curve (ii). m 2 ranges from to oo , but the table only supplies values from to 



x' z 

 14, since w 2 = \(n 3). x is found from x = 2 . 



C&2 



Curve (iii). m s ranges from 2'5 to oo , or our table will supply the probability 



x' z 



integrals of this curve from 2'5 to 15'5. The x is to be found from x = ^- 2 . 



w Hh as 



When the curve is written in the form 



the table will supply the probability integrals for n = 5 to 31. If we choose to 

 neglect the infinity of the fourth moment we can proceed to n = 2. 



z z 

 In the last form of this curve x = ^ 2 , or z z = #/(! x). The value of z z is 



given to five decimal places in the second column of each sheet of the table. This 

 enables the user to ascertain rapidly whereabouts he is in the #-variate for a given 

 value of z or 2 a . 



3. We need two kinds of interpolation into Table XXV: (a) we need to interpolate 

 between the tabulated values of n, and (6) we need to interpolate between the 

 tabulated values of x. Both these interpolations give rise to difficulties, which 

 require some consideration. 



* Actually the unpublished tables of the B-function carry us up to n = 101, m 3 =50-5, a value which 

 gives a much closer approximation to a normal curve. 



