230 



BIOLOGICAL EFFECTS OF RADIATION 



The theoretical distribution of deviations as obtained from the normal 

 probability curve and given in Table 3 is visualized in Fig. 1. The 

 abscissal scale shows the size of the deviations from the mean in units of 

 standard deviation. The total area under the curve is unity, and proba- 

 bilities, or relative frequencies, are measured in terms of the area between 

 the curve and the horizontal axis, appropriate to the probability question 

 asked. For example, the probability of the occurrence of a deviation 

 greater than the mean, of a size between one and two standard deviations, 

 is given by the area A BCD. We may compare Fig. 1 with Table 3 by 

 noting that the shaded area which represents deviations from the mean in 

 both directions, of a size greater than one standard deviation, constitutes 

 about one-third of the total area, the value given in Table 3 being 0.3173. 



With sampling variability expressed as in Table 3, it is possible for us 

 to determine an answer to the question as to the significance of the differ- 



Meoin * 1 



Deviation in Units of Standard Deviation 

 Fig. 1. — The normal probability curve. 



+5 



ence between the observed percentages. The first sample of size 608, if 

 drawn from a universe having a basic percentage of 49.7, would have a 

 standard deviation, 



= / (49.7)(50.3) ^ 2.0 per cent 

 \ 608 



For the second sample the standard deviation would be 



^ 1 (49.7) (50.3) =1.5 per cent 

 \ 1186 



We are interested, however, in the difference between these two samples 

 and we shall therefore need to consider not merely the sampling vari- 

 ability of a percentage as determined on a sample of a given size, but the 

 sampling variability of the difference between two quantities, the degree 

 of variability of each quantity being known. It can be shown that when 

 two quantities are independent, the standard deviation of the difference 

 between these quantities is given by 



