A frequent worry with multiple-choice questions (MCQ) is the
possibility of unearned success by lucky guessing. Studies of
guessing behavior report that "the great majority of examinees
do not engage in random guessing" and that "difficult items, as
might be expected, attract much more guessing than less
difficult ones." Consequently, "one can easily hypothesize that
when a guesser engages in random guessing, it is only on those
items which are too difficult for him" (Waller, 1973). An
empirical study confirms this and suggests a simple and
convenient solution. From Johnson O'Connor Research Foundation's
bank of 1,294 5-choice MCQ vocabulary items, 17 linked tests of
110 items each were constructed. Each test was administered to
400-600 students. The CAT System Software combined the raw data
from these 17 forms into one large data matrix in which
responses to items that persons did not encounter were marked as
missing. Rasch analysis of this 1,294 item by 7,711 student
response matrix produced a measure for e