Ideally, the (W/V) statistic allows comparison of one book's style to another. However, this simplistic metric is complicated by the simple fact that a short work will inevitably be denser than a larger work due to the fact that practically every word in a short work is unique. To understand, consider the case of writing a multi-million word essay. Given that there are only a limited number of words in the English language (~400,000 in this sample), one would eventually run out of words and thus the vocabulary density of such a titanic treatise would drop accordingly. This effect can be seen in the flattening trend of the scatter plots seen below.
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Scatter-plots of inverse vocabulary density (y-axis) vs. total words (x-axis). Samples below the pink trend line have denser vocabularies than average, those above, sparser. Note that trend line fits less well for smaller works. |
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In order that the vocabulary densities of large and small works may be compared, a 'normalizing' curve is fit to the sample creating a 'normalized density score' useful for comparison. Unfortunately, the one-size-fits-all trend curve (found empirically by minimizing least mean square error of a square-root scale coefficient) fails to fit the smaller works well as can be seen in Figure 3. Thus, comparison of large works (> 30,000 words) to smaller ones (< 30,000) is ill-advised. Therefore, the following tables isolate these two sample groups.
NOTE: Due to a change of server, I no longer have sufficient room to store the entire sample database on-line. My apologies.
Most Dense Vocabularies, Normalized For Book Size. Books Over 30,000 Words
Least Dense Vocabularies, Normalized For Book Size. Books Over 30,000 Words
Most Dense Vocabularies, Normalized For Book Size. Books Under 30,000 Words
Least Dense Vocabularies, Normalized For Book Size. Books Under 30,000 Words