The ideal difficulty index for a norm-referenced test is approximately 0.5. The difficulty index, often denoted as 'p', represents the proportion of test-takers who answered an item correctly. In a norm-referenced test, the primary goal is to differentiate among test-takers, comparing an individual's performance to that of a larger group.
An item with a difficulty index of 0.5 means that half of the test-takers answered it correctly and half answered it incorrectly. This mid-range difficulty maximizes the variance of scores, which is crucial for distinguishing between high and low achievers. If an item is too easy (e.g., p = 0.8 or higher), most students will get it right, providing little information about individual differences. Conversely, if an item is too hard (e.g., p = 0.2 or lower), most students will get it wrong, again failing to differentiate effectively. Therefore, items around 0.5 contribute most effectively to the overall reliability and discriminatory power of a norm-referenced test.