564 THE BELL SYSTEM TECHNICAL JOUKXAL, MARCH 1957 



p*2) are further from 0.5 and d* is small. For example, for fc = 4, P* = 

 0.95, p[i] = 0.95 and p[2] = 0.90 the value of n required for the alter- 

 native specification is 239 as compared to 850 observations per process 

 required to satisfy the original specification with the same P* and with 

 d* = 0.05. The alternative specification is justified on the basis of a priori 

 or previous information about the approximate values of the p's. 



REVERSING THE TABLES 



The experimenter may wish to use the tables of this paper in reverse. 

 For example, if n is fixed and d* is specified by the experimenter, then 

 by using the appropriate table he can find the probability of a correct 

 selection that is guaranteed for d ^ d*; i.e., a greatest lower bound to 

 the probability of a correct selection for d ^ d*. This process of re- 

 versing the given ^^alues and the values to be computed can most easih' 

 be carried out on graphs. For example, the above problem of finding the 

 guaranteed probability of a correct selection given d* and n is most easily 

 carried out on Figs. 18, 19, and 20. 



Appendix I 



MODIFICATION OF THE ORIGINAL SPECIFICATION 



The same value of n will, of course, satisfy the specification for dif- 

 ferent pairs of specified values (d*, P*). From a purely mathematical 

 point of view it is not necessary that d* should be the smallest difference 

 for which the experimenter desires to make a correct selection. For ex- 

 ample, if k = 3 the experimenter could specify any one of the four pairs 

 (0.10, 0.60), (0.25, 0.90), (0.30, 0.95) or (0.40, 0.99) and obtain the same 

 result, namel}^ n = 20. The experimenter may prefer to specify the curve 

 or set of points corresponding to a fixed n. Several such curves are given 

 in Figs. 18, 19, and 20 for k = 2, 3, and 4, respectively. The experi- 

 menter would decide in advance on some property of the curve that he 

 considers desirable and from the appropriate figure he could find the 

 curve with the smallest n-value that satisfies the desired property. 



The main point of the above paragraph is to point out that the original 

 specification in the body of the paper is one particular way, but not the 

 only way, of stating a specification that will determine a value of n. 

 The only criterion for a good way to state the specification is that the 

 experimenter should be able to bring his best judgment (or best guesses) 

 to bear on the quantities that have to be specified in advance. 



