Like many faculty, I am forced to give online exams for the first time this semester. (See I need help adapting my academic workflow to the COVID-19/coronavirus crisis – where do I start? for some related questions, though this question seems new.) I am being recommended to do various things like include an integrity pledge (honor code), make them timed, not use proctoring software, employ critical thinking questions, and make them open book. I plan to do the first 4, but my question is about the latter.
Namely, I have been thinking about various possibilities for what they are allowed to use for there exam. One could do any of the following, as well as some things in between: no resources, open book but nothing else, open book and personal notes and homeworks, open notes only, open book+notes+internet. I personally am leaning towards open book only. Now I can easily imagine that people would be more likely to cheat on a no resources exam versus open everything, and I imagine there are also differences compared to something like open book only. However, I have no idea to what extent there are differences (both in percentage of cheating and types of cheating), especially assuming things like time limits and honor codes.
Question: Have there been any studies about the differences in students' tendencies to cheat on non-proctored exams based on allowed resource materials?
I am not looking for personal speculation, but scientific studies, e.g., something like in this answer about a study on honor codes and cheating. I do not require the studies to include things like an honor code component, but it would be a plus. Even a basic study justifying universities' guidelines to make exams open book would be of interest.