One means of learning about the processes operating in a multiple choice test is to include some test items, called nonsense items, which have no correct answer. This paper compares two versions of a mathematical model of test performance to interpret test data that includes both genuine and nonsense items. One formula is based on the usual assumption that knowledge is all or none. The alternative formula incorporates the notion of partial knowledge adapted from signal detection theory. Results of a chemistry test taken by 407 subjects with four nonsense and 20 genuine items are used to compare the two formulas. A moderate correlation between the predictions and the findings indicate both model variations have some success, but the partial knowledge formula is the more accurate. (Author/BS)