836 BELL SYSTEM TECHNICAL JOURNAL 



If a syllable has two letter sounds, then the chance of perceiving 

 them both correctly is the same as the chance of perceiving the syllable 

 correctly or 



5 = U. (4) 



Similarly, for a syllable containing rn sounds 



5 = D\ (5) 



Or if A\, A2, Az, Ai ■ • • Am give the per cent of syllables in the list 

 containing 1, 2, 3, 4, • • • m sounds, respectively 



S= AiL + AoU- + A3L' + • • • A,nL"\ (6) 



Similarly, the chance of perceiving a syllable of the type con-vow 

 or vow-con is VC; of the type con-vow-con, con-con-vow or vow-con- 

 con is VC^; of the type con-con-vow-con, con-vow-con-con, vow-con- 

 con-con, or con-con-con-vow, is VC^, etc. 



For the old standard articulation lists these formul?e reduced to 



14 14 



s^^vc -\-jvr- = ^r- + 1^^ (7) 



For the new standard articulation lists they reduce to ^ 



5 = Va= U. (8) 



If a list of N syllables is used, then the letter errors and syllable 

 errors will be ?>N{\ — L) and N{\ — U), respectively, or the number 

 of letter errors per mistaken syllable, for the new standard lists, 

 will be 



^"= 1+L + L^- ^^^ 



It is seen that m approaches 3 as L becomes small, and unity as L 

 approaches unity. For L = .30, m = 2.06; for L = .50, m = 1.71; 

 ^ When derived from the probabiUty formulae 



VC- = LK 

 However, from the definition of V, C and L, 



L = (2C + F)/3 so that VC^ = L\ 

 The difference is 



(7-f-8C)(F- cy- 



d 



21 



Actually V and C are not wholly independent of each other and when values as 

 obtained in tests are substituted in the above equation, the difference turns out to 

 be small. 



