Quiz statistics calculations
General issues
Quizzes that allow multiple attempts
For quizzes that allow multiple attempts, by default the report should only include data from the first attempt by each student. Subsequent attempts probably do not satisfy the assumptions that underlie item analysis. However, there should be an option 'Include data from all attempts', which should have a disclaimer that this may be statistically invalid either near it on screen, or possibly in the help file. (For small data sets, it may be better to include all data.)
Using the first attempt also avoids problems caused by each attempt builds on last.
Within the analysis, when multiple attempts per student are included, each attempt is treadted as an independant attempt.
Adaptive mode
Adaptive mode does not pose a problem. We just assume that each item in the test returns a score, and these scores are added up to get the test score. That is, we use the item score including penalties in the calculation of the statistics.
Certainty based marking
Similarly, should CBM, and/or negative scoring for multiple choice questions be implemented, we just use the final item score in the calculations, making sure that the formulae are not assuming that the minimum item score is zero.
Incomplete attempts
There is an issue about what you do when not all students have answered all questions.