240 



BIOLOGICAL EFFECTS OF RADIATION 



cance of the difference between the two series as a whole by deriving the 

 difference divided by the standard error of the difference for each pair 

 of means and averaging these ratios. If there is no difference between 

 experimental and control groups, these ratios for a series of differences 

 should average to zero, with a standard deviation of unity. The standard 

 error of the average of these ratios will therefore be l/\/n, where n is 

 the number of pairs of values to be compared. If this mean is signifi- 

 cantly different from zero we may conclude that the entire series of obser- 

 vations indicates a significant difference between experimental and 

 control. 



The process may be illustrated by a set of observations from the paper 

 by Muriel Robertson (6), in which she compares at various times during 

 a growth period of 23 hr., the mean length of a sample of irradiated bodos 

 with a similar sample not irradiated. Table 6 presents the mean values 

 and their standard errors for the irradiated and nonirradiated groups at 

 five different times within the 23-hr. interval. 



Table 6. — Mean Lengths of Irradiated and Nonirradiated Bodos for 

 Different Times in a Twenty-three-hour Growth Period 



The ratio of the difference between these means to the standard error 

 of the difference is small enough so that at no point except possibly the 

 last one are we assured that the difference may not quite likely be due 

 to sampling. The average ratio of the difference to its standard error 

 is 1.502 and the standard error of this average is l/\/5 or 0.447. Thus 

 the average is 3.36 times its standard error and interpolating in Table 3, 

 we find that the probability is less than 1 in 1000 that such a series of 

 observations would arise by chance if no real difference between the irradi- 

 ated and nonirradiated group existed. Thus we may conclude that the 

 differences observed at the various times are really significant differences 

 in spite of the fact that they did not show up to be significant on the 

 basis of the individual tests. 



