Canal-U

Zipf's law in aphasia / Marjolein Van Egmond

Zipf's law in aphasia / Marjolein Van Egmond. In "Perspectives neuropsycholinguistiques sur l'aphasie - NeuroPsychoLinguistic Perspectives on Aphasia", colloque international organisé par l'Unité de Recherche Interdisciplinaire Octogone de l'Université Toulouse II-Le Mirail (France). Toulouse, 21-23 juin 2012.

In spontaneous speech, quantitative measures can provide valuable insight into general properties of words while generalizing over the content of the conversation. This renders it a suitable method to investigate word finding difficulties in aphasia. The quantitative measure employed in the current project is the distribution of word frequencies. Word frequencies in natural language texts typically conform to Zipf’s law, a power law P(k)~k ^α, where p(k) is the frequency of the k^th word if words are ordered by decreasing frequency. This law can also be formulated as p_ƒ~ƒ ^β, where p_ƒ is the proportion of words whose frequency is ƒ in a given sample text. Typically, it is found that α≈1 and β≈2.
The meaningfulness of Zipf’s law has been a topic of heated discussion. Zipf (1949) claimed that this word frequency distribution was due to the principle of least effort. But his opponents claimed that the statistics of simple random sequences of characters reproduce Zipf’s law equally well (e.g. Li, 1992; Miller & Chomsky, 1963). However, in both cases comparison between groups can reveal important differences between them.
Zipf’s law has been shown to apply to every natural language text in every language for which it has been tested (Baroni, 2008). The first to test Zipf’s law in aphasia were Howes and Geschwind (1964). They found that aphasic speech still conforms to Zipf’s law, but with a different slope. However, besides methodological issues, it is unclear where this difference arises: in function words only – for which problems in aphasic speech are well-known – or also in content words. This, therefore, was the goal of the present study, in which speech from people with non-fluent aphasia was analyzed.
Spontaneous speech of four Dutch non-fluent aphasic speakers was recorded and analyzed, and compared to speech of four healthy speakers from the Corpus of Spoken Dutch. Three analyses were made: one with full samples, one with only content words and one with only function words. Both α and β were measured.
For the α-analysis, it was found that Zipf’s law applies in all analyses. α was found to be significantly higher for aphasic speakers compared to healthy speakers. For β, Zipf’s law applies to all analyses for healthy speakers, but only to content words in people with aphasia; for function words it was found that Zipf’s law does not apply. In the content words analysis, β was significantly lower for aphasic speakers compared to healthy speakers. Interestingly, in the all-words analysis in healthy adults both α and β were found to be lower than the typically reported values.
We argue that β is more sensitive than α for mathematical reasons. We argue that our findings indicate that the mental lexicon of non-fluent patients is not qualitatively different from that of unimpaired populations. The deficit is due to reduced processing capacities in these patients, which affects lexical retrieval. The retrieval of function words is affected most.