How to motivate students to take a "gauge" test that helps us with statistics but does not contribute to their grade?
I have always seen this done not by issuing bonus points, but by issuing required points for taking the test, e.g. taking each test is work 5% of your grade. The poor students will do it for the free points, and the good students will do it to keep their grade up.
Don't be too focused on &quot;statistical validity.&quot; You're trying to reflect on your teaching, not publish a paper. You can look at who took the test(s) and how well they did, whether there was a bias in who self-selected. After all if the strongest students went from 0.8 to 0.95  on how good they were, there is not much room to examine your teaching: a ceiling effect. You will find room for improvement in  whether you are helping the weaker students effectively. They will respond for bonus points.