What is the optimal mean correct on a multiple choice test in order to maximise the measurement of individual differences? What is the optimal mean correct on a multiple choice test item in order to maximise the measurement of individual differences?
My understanding is that in general a percentage correct of 50% is optimal where there is no scope for guessing.
However, on multiple choice tests there is a certain number of response options. Thus, the probability of getting the correct answer if you know nothing, is one over the number of response options.

In this case I believe that the optimum is:

$$1/k + \frac{1 - 1/k}{2}$$

where k is the number of response options.

So the optimum for different values of k would be:


k = 2: optimum proportion correct = 0.75
k = 3: optimum proportion correct = 0.67
k = 4: optimum proportion correct = 0.625
k is infinite: optimum proportion correct = 0.50


That said, I'd still like to find the classic references where I obtained these ideas from. And I imagine item-response theory might have a little more to say about this, particularly regarding the common recommendation to vary the proportion correct over a range.

Furthermore, none of the above recommendations address the issue that setting the difficulty at the above level for most items can be intimidating for some test takers.