Analysing quizzes using a census.

This is a theoretical study of the marks that could be obtained from quizzes, when a census is done. The quizzes are limited to 'special' quizzes and we look at how many obtain a particular mark, and what happens to the distribution of marks when the guessing problem is tackled. Without building any tools we can do some calculations, but then we are driven to writing computer programs that calculate and display the distribution of marks. When computer programs are written they involve such large numbers that computer programs cannot normally handle them. Thus we are driven to languages, like C, where integers of an arbitrary size can be handled in libraries like LEDA. Quizzes can either have all their stems answered or have some of their stems missed. The philosophy of this study is to start off simply and gradually get more complicated, and so 'special' quizzes where all stems are answered are looked at first followed by 'special' quizzes where stems can be missed. The guessing problem is tackled, in this study, by: a) using negative marking, b) raising the pass mark, c) using a more complex quiz. What we find is that when the guessing problem of 'special' quizzes is exactly tackled the distribution of marks moves to the left (when the mean mark is 0), and that the tackling of the guessing problem leads to more problems. All 'special' stems include the answer, which can be guessed. The likelihood of guessing the correct answer to a stem decreases as the complexity of the quiz increases, but then the likelihood of passing also decreases. As the complexity of the quiz increases the distribution is 'bunched' at the lower end which means that half the marks of distribution are between the lowest mark and the mark where the mean occurs.The main conclusion is not quantitative but qualitative and is "Do not use 'special' quizzes for measuring understanding" because 'special' quizzes do not provide a space that allows one to demonstrate one's understanding and are therefore in-valid when understanding is claimed to be measured.