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A mathematical analysis is developed that relates to scores obtained in discrimination tests using consonant-vowel-consonant words. Account is taken of the fact that recognition of a speech sound depends on “intrinsic” and “contextual” factors. The intrinsic factors are the acoustical properties of the sound and its probability of occurrence. Two contextual factors are introduced: a “second-order” factor, including acoustic influences in adjacent sounds and second order phoneme probabilities, and a “vocabulary” factor. The theory is applied to the results of discrimination tests given to two groups of children, one normally hearing, the other partially hearing. The vocabulary factor is found to be related to age only, while the second-order factor is related to high-frequency hearing loss. This implies that the second-order factor is primarily an acoustical one. Comparisons are shown between measured discrimination scores and the scores which would theoretically be obtained if only intrinsic factors contributed to discrimination. These show that a score based on the percentage of recognized phonemes is more valid as a measure of the ability to make phonemic classifications from intrinsic acoustical clues, than is a score based on the percentage of recognized words.
Arthur Boothroyd (Thu,) studied this question.