STATISTICAL TREATMENT 



229 



Before concluding that the mortaUty rate at intensity 5.5 r per min. is 

 greater than that at 2.8 r per min. we must test the statistical significance 

 of the difference between these two percentages. This question can be 

 framed as follows : How probable is it that if two random samples of sizes 

 608 and 1186 were drawn out of a universe or experience having a basic 

 mortality of 49.7 per cent, they would differ as much in their mortality as 

 they do in the present illustration? We ask this question because if we 

 find it quite likely that two random samples would exhibit a difference at 

 least as great as in the present case when these samples were drawn out 

 of the same experience, we shall hesitate to conclude that this observed 

 difference is due to anything other than chance. 



To answer this question we need to know something of the variability 

 of percentages determined by a number of samples of the same size, all 

 drawn from the same experience. For a complete discussion of this 

 subject the reader is referred to the treatment of the point binomial in 

 any standard textbook on statistical method. It will be sufficient to say 

 here that theoretical considerations and experimental tests have show^n 

 that such percentages are distributed in a normal probability curve, 

 having a mean equal to p and a standard deviation equal to the square 

 root of pq/71, where 



p = the percentage in the universe sampled. 



q = 100 - p 



n = size of sample drawn. 

 Since the normal curve is completely determhied by its mean and standard 

 deviation, it is possible, having determmed these constants, to state the 

 distribution of deviations of varying size. Table 3 gives the probability, 

 P, that a sample will deviate from the central position by an amount equal 

 to, or greater than, any multiple of the standard deviation, a. 



Table 3. — Probability of Occurrence of Deviations of Varying Size, as Given 



BY THE Normal Probability Curve 



