Abstract
Perhaps the most qualitatively interpretable vocabulary test score is an estimate of the total number of words the learner knows in the tested domain, such as a frequency word list, or vocabulary taught as part of a course curriculum. In cases where it is not possible to test the entire domain word-for-word, vocabulary tests such as the vocabulary levels test (Nation, 1990) and vocabulary size test (Beglar, 2010, Nation & Beglar, 2007) typically employ a polling method, in which total vocabulary size is inferred from a sample of tested words. A drawback of this method is that it assumes the tested words are randomly sampled from and therefore representative of the tested domain, which can affect test reliability in cases where there are many words in the domain that are far below or above learners’ ability. This paper outlines an alternate method for estimating vocabulary size from a test score using item response theory, which allows estimation of total vocabulary size from a nonrandom sample of words well matched to learners’ ability, resulting in tests of practical length with high reliability that can be used to estimate the total number of words a learner knows. Such a test scoring method, currently in use at a private university in southern Japan, is used as an example.

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