vocd: A theoretical and empirical evaluation

A reliable index of lexical diversity (LD) has remained stubbornly elusive for over 60 years. Meanwhile, researchers in fields as varied as stylistics, neuropathology, language acquisition, and even forensics continue to use flawed LD indices — often ignorant that their results are questionable and in some cases potentially dangerous. Recently, an LD measurement instrument known as vocd has become the virtual tool of the LD trade. In this paper, we report both theoretical and empirical evidence that calls into question the rationale for vocd and also indicates that its reliability is not optimal. Although our evidence shows that vocd's output (D) is a relatively robust indicator of the aggregate probabilities of word occurrences in a text, we show that these probabilities — and thus also D — are affected by text length. Malvern, Richards, Chipere and Durán (2004) acknowledge that D (as calculated by vocd's default method) can be affected by text length, but claim that the effects are not significant for the ranges of text lengths with which they are concerned. In this paper, we explain why D is affected by text length, and demonstrate with an extensive empirical analysis that the effects of text length are significant over certain ranges, which we identify.