SELECTING THE BEST ONE OF SEVERAL BINOML\L POPULATIONS 561 

 COMPARISON OF THE T\\^0 SPECIFICATIONS 



It should be pointed out that for a given Z; the same value of n would 

 satisfy the specification for different specified triplets 



For example with k = 4, P* = 0.85 and n fixed we could vary p*] in 

 the alternative specification and compute for each p[i] the correspond- 

 ing largest value of p*2] such that the specification (P*, p*j , p*o]) is 

 satisfied. This is shown in Fig. 17 for n = 5, 10, 20 and 60. The vertical 

 distance in Fig. 17 between the appropriate curve and the 45° line 

 (n = 3c) is the length of the indifference zone (p[i] , P[2]). The indif- 

 ference zone widens in the center and narrows at both ends. In fact we 

 find just as in the original specification that for n greater than (say) 4 

 the indifference zone is widest when p* ] and p* ] are symmetrical about 

 0.5. It is clear that the two specifications would coincide if we took d* in 

 the original specification and set p*] = § (1 + d*), p[2] = | (1 — d*) 



1.00 



0.95 



0.90 



0.85 



0.80 



0.75 



0.70 



0.65 



0.60 



0.55 



0.50 



0.5 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 



d 



Fig. 18 — Probability of a correct selection as a function of tlie true difference 

 '^ — V\\\ ~ P[3] under the least favorable configuration for k = 2 and selected 

 values of n. 



