STATISTICAL TREATMENT 247 



The only additional computation necessary for the determination of 

 r after the means and standard deviations have been derived is the 

 multiplication of each x value by the corresponding y value, the summa- 

 tion of these products, and the division of this sum by the number of 

 pairs of values involved. When there are a relatively small number of 

 pairs of observations as is the case in this illustration, this calculation 

 may be done directly, but if the number of observations is very much 

 greater, the arithmetic procedure may be simplified by making use of a 

 correlation table and by its treatment as outlined in standard textbooks 

 on statistical method. 



Applying the direct method to the observations in Table 8, we have 

 the following results. The mean systolic pressure before radiation is 

 185 mm. ; the variation in these initial readings is indicated by a standard 

 deviation of 14 mm. ; the mean drop in pressure is 9.1 mm. ; and the stand- 

 ard deviation of this drop is 10.9 mm., indicating a high degree of varia- 

 tion in the effect of the radiation on different days. The correlation 

 between the drop in pressure and the initial pressure is indicated by the 

 coefficient of correlation, r, of 0.32. The values of a and b as determined 

 by the above equations are —37.4 and 0.25, respectively, so that the 

 equation relating the drop in pressure to the initial pressure is 



y = 0.25x - 37.4 



This equation written in the form 



y = 0.25(x - 150) 



shows that when the systolic pressure before radiation was 150 mm., 

 the average drop was zero, and that for initial pressures below 150 mm., 

 the average drop was negative, indicating a rise in pressure on the average, 

 after radiation. The value of the h constant shows that for each unit 

 that the initial pressure stood above 150 mm. the drop increased on the 

 average 0.25 mm. Thus we have in two statistical constants a and h 

 a statement of the way in which, for this individual, the average drop 

 in systolic blood pressure following radiation changed according to the 

 initial pressure. 



In a similar way we might study the variation of drop in systolic 

 pressure according to duration of irradiation, and the results of the two 

 solutions might be thrown together by the method of partial correlation, 

 as outlined in any standard text. The satisfactory statistical treatment 

 of this problem in a general sense would involve the determination and 

 analysis of a series of h constants for a variety of patients. 



Other than the straight line, the most commonly used equational 

 relationship is the exponential form, or the equation for geometric 



