vocd-D (D Measure)
Also known as: vocd-D, D Measure, vocd, HD-D
vocd-D, also called the D measure, is a length-robust index of lexical diversity developed by David Malvern and Brian Richards. Instead of reporting a single type-token ratio, it characterizes how a text's TTR falls as sample size grows and fits that empirical curve to a one-parameter probabilistic model; the fitted parameter D is the diversity score, with higher D meaning richer vocabulary. HD-D, introduced by McCarthy and Jarvis, is the mathematically exact, sampling-free counterpart that computes the same underlying quantity directly from the hypergeometric distribution.
Key highlights
- Models the length dependence of TTR explicitly rather than ignoring it, yielding scores comparable across texts of different lengths.
- Grounded in an explicit probabilistic theory of vocabulary use, giving the parameter D a clear interpretation.
- HD-D is exact and deterministic, eliminating the random-sampling variability of the original vocd-D for fully reproducible results.
- Well validated and widely adopted, with strong tool support and a large body of comparative literature including developmental norms.
Intuition
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How it works
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When to use it
Use vocd-D or, preferably, HD-D when you need to compare lexical diversity across texts of unequal length and want a measure grounded in an explicit model of vocabulary use. The approach suits learner-corpus and child-language research, clinical language sampling, and any comparison where trimming texts to equal length is undesirable. Prefer HD-D over the original sampling-based vocd-D for reproducibility, since vocd-D returns slightly different values on repeated runs. Texts should not be too short — sampling at N up to 50 requires a comfortable margin above that — and it is good practice to report vocd-D/HD-D alongside MTLD, which captures a complementary, sequential view of diversity.
Strengths & limitations
- Models the length dependence of TTR explicitly rather than ignoring it, yielding scores comparable across texts of different lengths.
- Grounded in an explicit probabilistic theory of vocabulary use, giving the parameter D a clear interpretation.
- HD-D is exact and deterministic, eliminating the random-sampling variability of the original vocd-D for fully reproducible results.
- Well validated and widely adopted, with strong tool support and a large body of comparative literature including developmental norms.
- The original vocd-D relies on random sampling, so repeated runs on the same text give slightly different D values unless many runs are averaged.
- Both versions assume a particular probabilistic model of word use and ignore the order and clustering of words within the text.
- Estimates are unreliable for short texts, since the sampling range (up to 50 tokens) needs a text comfortably longer than that.
- Like all type-based measures, results depend on tokenization, lemmatization, and proper-noun handling, which must be standardized across compared texts.
Common pitfalls
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Applications
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Frequently asked
What does the parameter D actually mean?
D is the single parameter of the probabilistic model that best reproduces how the text's TTR falls as sample size grows. A higher D means the TTR curve sits higher and declines more gently — that is, the vocabulary is depleted more slowly as you sample more words — so larger D corresponds to greater lexical diversity. Because D is fitted to the whole curve rather than read off a single ratio, it is comparable across texts of different lengths, which is the entire point of the measure.
What is the difference between vocd-D and HD-D?
They estimate the same underlying construct, but by different means. vocd-D draws many random samples to build an empirical TTR curve and then fits the model parameter D to it, which introduces sampling variability so that repeated runs differ slightly. HD-D instead computes the exact hypergeometric expectation that the sampling was approximating, summing over each word type the probability that a random sample contains it. HD-D is therefore deterministic and reproducible, and McCarthy and Jarvis recommend it as the principled replacement for vocd-D.
Should I report vocd-D/HD-D or MTLD?
Both are length-robust and they capture overlapping but distinct aspects of diversity, so reporting both is common and recommended. vocd-D/HD-D is grounded in a probabilistic sampling model, while MTLD reflects the sequential rate at which a running TTR decays. McCarthy and Jarvis found MTLD the most length-stable of the established measures and pair it with HD-D in their recommendations. If you must choose one diversity-via-sampling measure, prefer HD-D over the original vocd-D for its exactness and reproducibility.
Sources
- 1.Malvern, D., Richards, B., Chipere, N., & Durán, P. (2004). Lexical Diversity and Language Development: Quantification and Assessment. Palgrave Macmillan.ISBN 9781403902313
- 2.McCarthy, P. M., & Jarvis, S. (2007). vocd: A theoretical and empirical evaluation. Language Testing, 24(4), 459–488.
- 3.McCarthy, P. M., & Jarvis, S. (2010). MTLD, vocd-D, and HD-D: A validation study of sophisticated approaches to lexical diversity assessment. Behavior Research Methods, 42(2), 381–392.
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Cite this page
ScholarGate. (2026, June 22). vocd-D (D Measure). ScholarGate. https://scholargate.app/linguistics/vocd-lexical-diversity