Do certificates from accredited online courses play any role in applying for a graduate program?
This is a personal view and I think that there would be a lot of variation in what people accept for a graduate program; especially for a doctoral program.
I would tend to discount almost all such courses for the simple reason that I have no real idea about what the student learned in the course, independent of whatever grade the received. I have no idea what they did and I have no idea how to evaluate a course that relies only on online quizzes and tests. To me, the value of a certificate is just that of a piece of paper. Probably virtual paper, actually.
I would think that such courses are fine for the person who simply wants to learn something and is willing to do a lot of work (exercises, projects,...) based on it, but not for any &quot;accreditation&quot; purposes.
The exception would be a reasonably scaled course with a professor and sufficient staff so that the student/staff ration is less than 30/1, preferably closer to 20/1. Most online courses don't have that characteristic (though Harvard's CS50 does, actually, as do courses run by Open University in UK).
A person learns through reinforcement and feedback. Massive online courses have no real way to judge whether such learning has happened. The reinforcement can't be enforced (so to speak) and the feedback to the student is minimal. An individual might be able to judge that they, themself, learned something, but an outsider would find it difficult to impossible.
I can't guarantee (or even guess) how many feel similarly, but the educational background of most of the people judging things now is very different from such massive &quot;courses&quot;.
I don't think they are worthless, though it is impossible for me to make a judgement about their worth with enough confidence to predict the success of a student in a graduate program (especially, again) at the doctoral level. I would base my judgement on other factors, and especially those of recommenders.