Entropy as a measure of mixedupness of realizations in child speech

Typical morpho-phonological measures of children's speech realizations used in the literature depend linearly on their components. Examples are the proportion of consonants correct, the mean length of utterance and the phonological mean length of utterance. Because of their linear dependence on their components, these measures change in proportion to their component changes between speech realizations. However, there are instances in which variable speech realizations need to be differentiated better. Therefore, a measure which is more sensitive to its components than linear measures is needed. Here, entropy is proposed as such a measure. The sensitivity of entropy is compared analytically to that of linear measures, deriving ranges in component values inside which entropy is guaranteed to be more sensitive than the linear measures. The analysis is complemented by computing the entropy in two children's English speech for different categories of word complexity and comparing its sensitivity to that of linear measures. One of the children is a bilingual typically developing child at age 3;0 and the other child is a monolingual child with speech sound disorders at age 5;11. The analysis and applications demonstrate the usefulness of the measure for evaluating speech realizations and its relative advantages over linear measures.