The spaced repetition software system Anki is the de facto standard for foreign language vocabulary learning. Its algorithm requires lots of performance data to schedule flashcards in the most efficient way. Anki displays these statistics in a group of thorough and informative statistical graphs and descriptive text.
The premise is that you can run your own more extensive experiments and statistical tests on the data once you have it in hand. A bit of technical expertise is needed to get it operational but if you are up to it, clone the github repos above and go for it.