Information transfer analysis: a first look at estimation bias.

Information transfer analysis [G. A. Miller and P. E. Nicely, J. Acoust. Soc. Am. 27, 338-352 (1955)] is a tool used to measure the extent to which speech features are transmitted to a listener, e.g., duration or formant frequencies for vowels; voicing, place and manner of articulation for consonants. An information transfer of 100% occurs when no confusions arise between phonemes belonging to different feature categories, e.g., between voiced and voiceless consonants. Conversely, an information transfer of 0% occurs when performance is purely random. As asserted by Miller and Nicely, the maximum-likelihood estimate for information transfer is biased to overestimate its true value when the number of stimulus presentations is small. This small-sample bias is examined here for three cases: a model of random performance with pseudorandom data, a data set drawn from Miller and Nicely, and reported data from three studies of speech perception by hearing impaired listeners. The amount of overestimation can be substantial, depending on the number of samples, the size of the confusion matrix analyzed, as well as the manner in which data are partitioned therein.