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Answer by Scott E. Fahlman, research professor of computer science and language technolgies, Carnegie Mellon:
I think this is sort of the wrong question. The main purpose of letters of recommendation is to allow the admissions committee and potential faculty advisers to judge your ability to “turn the corner” from just taking classes and to start doing actual research.
Perhaps the strongest evidence is any sort of publication or report on some project you've done. Good external letters that address your performance on research or quasi-research projects (ones that at least require some initiative, independence, and a little creativity) are also strong evidence. And then your statement of purpose ties all that together and puts it in context.
A letter from a faculty member that just says that you took his class and did well doesn't count for much of anything. We can tell that much from your grades. A good letter writer will strain to come up with something more—“We had some good after-class discussions, and I noticed that X always helped out the other students”—and that is a slight positive but doesn't address the research question.
Of course, a negative letter, from anyone, can hurt you. We very seldom see letters that are truly negative: “X is not very bright, a complete pain to work with, the other students hate him, and he dropped the ball on his project, screwing the rest of us.” But faculty doing admissions become quite sensitive to language that recommenders use when they really have nothing good to say, but are too polite to say anything really bad. (Hint: If you ask a faculty member or boss to write you a letter and you sense any significant reluctance, don't press the matter—you'll get one of these “damning with faint praise” letters, and it won't help you.)
So what makes a positive letter? It should describe some research or research-like project that you've worked on and that the letter writer participated in or observed first-hand. It should make clear which parts were your responsibility and initiative and what's useful or interesting about what you accomplished. There should be some detail and some real enthusiasm. If all you've got is “I told X to do the following, and he completed the work successfully,” that's better than nothing, but if the writer can highlight your creative contributions (direct or via helping others on the project), that's much better.
If the letter is from a faculty member at a good university, it helps a lot if the writer says he would really love to accept you as a grad student (or already has), but there may be valid reasons for you to continue your work elsewhere. Often, these people are in a good position to compare you with other students we have accepted from their university and who did well.
Of course, letters from researchers (faculty or in industry) whom we know directly or at least by reputation carry a lot more weight than letters from people we don't know. Maybe that's unfair, but it's the way the world works.
It's really hard when we get a letter that says, “In my 35 years as a CS professor in the University of Northern Paraguay, X is by far the most gifted student I've ever worked with, and his scientific insights were inspiring to me.” We just don't know how to calibrate that. Assuming that description is sincere, we still don't know how X compares with an average graduate of CMU or MIT. It's a bit better if the letter says, “I spent two sabbatical years at Stanford, working with Y and Z, and I would say that X is a talent in the same league as those people.” And it's better still if the writer is known to (and respected by) someone on our faculty, and someone can say, “This is better than the letters he usually writes.”
So industry versus academic recommenders is not the key issue—it's whether you did a research-like project with the person and whether we have some reason to trust his or her opinion.
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