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.

Inspontaneous speech, quantitative measures can provide valuableinsight into general properties of words while generalizing over thecontent of the conversation. This renders it a suitable method toinvestigate word finding difficulties in aphasia. The quantitativemeasure employed in the current project is the distribution of wordfrequencies. Word frequencies in natural language texts typicallyconform to Zipf’s law, a power law P(k)~k α,where p(k)is the frequency of the kthword if words are ordered by decreasing frequency. This law can alsobe formulated as pƒ~ƒ β,where pƒis the proportion of words whose frequency is ƒ in a given sampletext. Typically, it is found that α≈1and β≈2.
Themeaningfulness of Zipf’s law has been a topic of heated discussion.Zipf (1949) claimed that this word frequency distribution was due tothe principle of least effort. But his opponents claimed that thestatistics of simple random sequences of characters reproduce Zipf’slaw equally well (e.g. Li, 1992; Miller & Chomsky, 1963).However, in both cases comparison between groups can reveal importantdifferences between them.
Zipf’slaw has been shown to apply to every natural language text in everylanguage for which it has been tested (Baroni, 2008). The first totest Zipf’s law in aphasia were Howes and Geschwind (1964). Theyfound that aphasic speech still conforms to Zipf’s law, but with adifferent slope. However, besides methodological issues, it isunclear where this difference arises: in function words only – forwhich problems in aphasic speech are well-known – or also incontent words. This, therefore, was the goal of the present study, inwhich speech from people with non-fluent aphasia was analyzed.
Spontaneousspeech of four Dutch non-fluent aphasic speakers was recorded andanalyzed, and compared to speech of four healthy speakers from theCorpus of Spoken Dutch. Three analyses were made: one with fullsamples, one with only content words and one with only functionwords. Both αand βwere measured.
Forthe α-analysis,it was found that Zipf’s law applies in all analyses. αwasfound to be significantly higher for aphasic speakers compared tohealthy speakers. For β,Zipf’s law applies to all analyses for healthy speakers, but onlyto content words in people with aphasia; for function words it wasfound that Zipf’s law does not apply. In the content wordsanalysis, βwassignificantly lower for aphasic speakers compared to healthyspeakers. Interestingly, in the all-words analysis in healthy adultsboth αand βwere found to be lower than the typically reported values.
Weargue that βis more sensitive than αfor mathematical reasons. We argue that our findings indicate thatthe mental lexicon of non-fluent patients is not qualitativelydifferent from that of unimpaired populations. The deficit is due toreduced processing capacities in these patients, which affectslexical retrieval. The retrieval of function words is affected most.