Pollack and Decker, 1960

Irwin Pollack and Louis Decker, Consonant Confusions and the constant ratio rule, Language and Speech 3:1-6, 1960

The aim of the paper is to test Clarke's Constant Ratio rule that models how values in confusion matrices are affected by the phonemes involved, by testing sets of 2, 4 and 8 phonemes. I'm not convinved by their analysis suggesting the rule is valid, and wish they had given at least some of their 2x2 and 4x4 matrices. It's not much use saying, for example, that the average absolute difference between entries in the 4x4 matrix (for /lrwy/ at -5 dB) and what would be predicted using the 8x8 matrix is 3.7 when the average entry in the matrix is 5.9.

They did give 8x8 matrices, which are given here. What's nice about these is that they are mostly liquids and glides and even a Null.

Specifically, CV syllables were tested, with the vowel V being /a/. This was in a carrier phrase "You will trah, ___". The values of C were /f/, /h/, /l/, /r/, /w/, /j/, /hw/ and the absence of a consonant /#/.

Four S/N ratios were used. Six subjects served alternately as talkers and listeners. Each stimulus was tested 360 times; the matrices have percentage values. In other words, the (i,j)-th entry has the percentage of times a /i/ stimulus was heard as /j/. Row totals may not be 100 owing to rounding errors.

Here are the matrices, at each S/N level.

An example is the matrix for S/N = -5 dB.

>> pd5 = phonmat ('html/pollackdecker5.dat');
>> pd5.total

 pm (object of type PHONMAT) = 

    title: Consonant Confusions at S/N of -5 dB (Pollack & Decker, 1960. All values percentages.
    Phones involved: 8, namely f h l r w H (hw) y # (no null none) 

       f  h  l  r  w  H  y  #     Total
    f  96 0  0  1  2  0  0  0   f 99
    h  6  84 0  0  0  0  0  9   h 99
    l  1  1  76 12 5  2  2  0   l 99
    r  1  1  11 57 14 5  11 0   r 100
    w  1  0  3  5  69 15 8  0   w 101
    H  1  1  2  3  25 62 7  0   H 101
    y  0  1  1  1  3  1  94 0   y 101
    #  2  6  0  0  1  0  0  91  # 100