238 BIOLOGICAL EFFECTS OF RADIATION 



a statistical constant called coefficient of variation and defined as 



100(7 



C. of V. = 



m 



this index number stating the variability as a percentage of the mean. 

 The standard error of the coefficient of variation is given approximately by 



_ C. of V. 



In the illustration under consideration the difference between the coeffi- 

 cient of variation in the irradiated and that in the nonirradiated group 

 is 0.60 with a standard error of 0.76. The difference is thus only 0.8 

 of its standard error and there are approximately 40 chances in 100 that 

 such a difference would arise from simple sampling. We shall therefore 

 call this difference insignificant and conclude that, relative to their means, 

 the irradiated and nonirradiated animals show the same degree of 



variation. 



The statistical constants that have been derived may be seen in 

 graphical relationship to each other and to their respective frequency 

 distributions in Fig. 2. 



Since the distribution of frequency is so often compared with that of 

 the normal probability curve, a paper has been designed for the graphical 

 treatment of frequency problems. This paper is called arithmetic proba- 

 bility paper and has for one axis a uniform scale representing the scale 

 of measurement and for the other axis a scale of accumulated percentages, 

 this scale being so adjusted that for normally distributed material the 

 accumulated percentages of the frequency plot as a straight line. To 

 apply this paper to the present illustration we have given in Table 5 the 

 accumulated frequency stated as percentage of the total and these 

 accumulated frequencies are shown on arithmetic probability paper in 

 Fig. 3. On the vertical scale of this figure we have the length in 0.5/i 

 and on the horizontal scale we have a statement of the percentage of 

 individuals occurring below the indicated length. The points for the 

 irradiated and nonirradiated forms fall approximately on straight lines, 

 indicating that the distributions of the measurements are nearly normal. 

 Straight lines have been drawn through these points, more attention being 

 paid to the points in the center, since points at the extremes are always 

 subject to a higher degree of variation on this paper. 



Not only can this paper be used to test whether a distribution approxi- 

 mates the normal curve, but it can also be used as a computing device. 

 Since the distributions are approximately normal the means will be at the 

 50 per cent position, and reading the length corresponding to this point 



