What's a good measure of spread near a threshold?

I am choosing summary statistics for percentage data that is clustered near 100%. Each subject takes the same test twice. Each test consists of at least 40 questions. I want to be able to predict which subjects will improve more. I have a hypothesis that subjects with higher variability of performance in the first test will improve more. To test this, I computed the variance of each subject's per-question scores, and indeed those with higher variance improved more. But the problem is that the presence of the threshold introduces an artefact: subjects with near-100% performance to start with can't improve much and also may have lower variance simply because the upper tail of question scores is limited by the maximum score threshold. Inter-quartile range would suffer from the same problem. I will try "one-sided variance" (using only question scores lower than the mean), and "lower quartile to median range". Any other ideas, and does anyone know of a use in the literature of something like this?

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A test result is partly the effect of mistakes on individual items and can approximately be modeled as a Binomial outcome. For the Binomial, the variance will be greatest for scores near 50% and will decrease to 0 at 0% and 100%. This alone could explain your hypothesis--and would indicate it might say nothing meaningful about the test or its subjects. So the first thing you ought to do is check this out. One way is to attempt to stablilize the variance with a logit or logit-like transformation of the scores. This will automatically address the other issues you raise. –  whuber Oct 26 '12 at 16:38
What do you mean by "variability of performance"? To me, this would imply variation from one test to another, not from one question to another. As @whuber astutely points out, with questions that are are marked either right or wrong, the variance is directly related to the mean (intuitively, a person who gets every question right clearly has no variability). –  Peter Flom Oct 26 '12 at 17:15
Good catch, @Peter. Perhaps these are not binary questions, but are given partial credit, so if all questions in a test have the same value and the same (intended) level of difficulty, one could identify and measure variability even within a given test. (But the insight provided by the analysis of binary tests, where questions are either correct or not, is still useful.) –  whuber Oct 26 '12 at 17:21
That's certainly possible, but partial credit scoring seems pretty rare, in my experience. –  Peter Flom Oct 26 '12 at 17:34