246 BIOLOGICAL EFFECTS OF RADIATION 



radiation. For the purposes of this illustration we shall treat the 

 measurements on subject F which are presented in Table 8. 



Although the effects of radiation are in this case given in terms of 

 two measurements, blood pressure before and after radiation, the fact 

 that we are interested in the possible rise or fall in blood pressure would 

 lead us immediately to a consideration of the difference between the two 

 pressures. If we form this difference for the 55 visits for which treatment 

 was given, we find that there was an average fall in pressure of 9.1 mm. 

 Hg. If this fall in pressure had occurred uniformly throughout the 

 series of observations, it would only be necessary to determine its degree 

 of variation and the problem would be resolved by the treatment of one 

 variable alone, that is, the fall in pressure. Examination of the measure- 

 ments, however, shows that there is a decided tendency for the larger 

 falls to occur in the cases where the initial pressure was high, and we must 

 therefore consider the difference in relation to the initial pressure. By 

 plotting the fall in pressure against the initial pressure for each of the 

 observations, we see that they are not in direct ratio to each other, and 

 therefore a treatment of the drop in pressure as a percentage of the initial 

 reading would be inappropriate. We may, however, derive an equational 

 relationship that will give us the average drop in pressure for each initial 

 pressure by treating this as a problem in simple linear correlation. 



Simple linear correlation analysis merely means the determination of 

 a straight line to represent the average values of one variable for given 

 values of the other, and of some measure of the degree of variation of the 

 points about the line. This solution may be outlined as follows: Let y 

 represent the fall in pressure and x the initial pressure. Then a linear 

 relation between these variables may be represented by the equation 



y = a -]r hx 



in which a is dependent upon the choice of origin and is therefore rela- 

 tively unimportant, and h represents the change in the fall of blood 

 pressure for each unit change in the blood pressure itself. The values 

 of a and 6 derived by the method of least squares will be given by the 

 following equations: 



a = niy — hnix 

 6 = r— 



where nix, niy, Cx, ay, represent the means and standard deviations of 

 X and y as defined in the section treating measurements, and r is called 

 the coefficient of correlation and is given by the formula 



(Xxy/n) — ntxtny 

 r = 



<Jx(Ty 



