STATISTICAL TREATMENT 231 



Applying this equation to our case, we have 



(Tdiff = V(2.0)- + (1.5)2 = 2.5 per cent 



Thus we have two samples, one giving a death rate of 40.1, the other a 

 death rate of 54.6 per cent. The difference between these two death 

 rates is 14.5 per cent and the standard deviation of this difference as 

 derived above is 2.5 per cent. The difference measured in units of 

 standard deviation is therefore 



diff. ^ 14.5 ^ ^ g 

 Cdiff 2.5 



Taking this value into Table 3, we see that the probability of these two 

 samples coming out of the same experience is less than 0.00000001. Thus 

 it is extremely improbable that these two death rates are samples out 

 of the same universe and we feel with a high degree of certainty that the 

 mortality rate at intensity 2.8 r per min. is definitely less than the 

 mortality rate at intensity 5.5. 



A similar comparison of the death rates at intensity 5.5 r per min. and 

 22.0 r per min. gives a probability of 0.47 that a difference at least as great 

 as the observed would occur when two samples of sizes 1186 and 2340 are 

 drawn out of the same experience (53.7 per cent). Thus we hesitate to 

 say that there is a real difference in the effect of these two intensities since 

 there is such a large probability that the observed difference might arise 

 from sampling alone. 



An examination of all the succeeding intensities in Table 1 shows 

 that the death rates fluctuate about a value in the neighborhood of 

 50 per cent. We might test these in successive pairs by the method just 

 outlined, but since they have so little variation, we should like to test 

 them as a group. We may do this by asking whether the death rates 

 for the intensities 5.5 to 4690 r per min., inclusive, differ from each other 

 by amounts that are greater than would be expected under sampling. To 

 answer this question we need the death rate for the entire experience 

 covered by these intensities. The total number of eggs observed being 

 15,541, and the number of deaths, 8223, this death rate is 52.9 per cent. 

 Using this general death rate, 52.9 per cent, as the value of p and taking 

 the number of eggs at each intensity as n, we can calculate the standard 

 deviation for each death rate and then determine how far each death rate 

 deviates, in multiples of its standard deviation, from the general death 

 rate. These 12 results are given in Table 4, together with the expected 

 number in each class, determined by applying the probabilities obtained 

 from Table 3. 



The agreement between the observed results and those expected 

 under simple sampling would lead one to say that there is a high degree of 



