How big is my vocabulary? In other words, how many English words do I know. We will define this objectively to be the number of words listed in a given dictionary which I ``know.'' To estimate this, I will obtain a simple random sample of pages from the dictionary and count the number of words on each of the sampled pages which I know. From this, I can estimate the average number of words per page which I know. Then, mulitplying by the total number of pages in the dictionary (only counting the ones used for the list of words and definitions), I can estimate my vocabulary.
Of course, I would like to know how accurate my estimate is.
I could also do something like estimate the total number of German words I know (in a similar fashion, using my German/English dictionary) and the total number of Spanish words, and test to see if I know significantly more German words than Spanish words.
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Send problems or suggestions to dcox@stat.rice.edu