The connection between item bias and test scores was investigated using a simulation approach. Two samples of hypothetical examinees were simulated using an item response theory model. The two samples were identical, except that the mean theta value 1 sample was 5 less than the other. The simulated tests consisted of 50 items with characteristics which varied with the difficulty of the test for the group, the distribution of 6 values, the mean discrimination of items, and the condition of bias. The study resulted in several hypotheses concerning desirable characteristics of tests given that the actual amount and condition of bias in the tests is unknown: (1) the differences in true score between groups was larger with the peaked distribution than with the uniform distribution; (2) tests with relatively low discrimination appear to produce larger differences; (3) tests which are relatively easy for the high scoring group should have more rectangular distributions; (4) tests which are quite difficult seem to produce smaller differences when they are peaked; and (5) for tests with medium or high average discrimination, tests with difficulty centered between the groups appear to be least likely to produce inflated differences due to bias. (Author/BW)