This may be as good time as any to plug my calculator for finite resistor networks (including grids) [1]. It works by eliminating non-terminal nodes one by one with the Star-Mesh transform, while keeping the exact rational resistances at each point.
EDIT: To clarify, patch out just the polyfill (the first line in the snippet). You can of course keep using MathJax, and the second line alone should be enough. (Though still better host a copy by yourself, just in case).
The study is based on a web questionnaire, answered by 589 out of 2552 Ph.D. students. The mental health of the remaining 1963 students who did not take the survey is very likely to be in worse shape than of those who did.
In discussion the authors say "Moreover, we want to emphasize the likely sample bias in our data. We recruited participants mainly via mailing lists and our project therefore probably has especially appealed to people who are already interested in health or aware of mental health issues."
I guess this bias could be significant. I can't imagine that someone who is particularly stressed, depressed and sleep-deprived will pay attention to a mailing list message that has anything to do with mental health, or aks "How's your PhD going?". Personally, if I saw such email, I would close it and forget it as fast as I possibly could.
Another problem is that people tend to lie to themselves about their mental health issues, telling themselves that it's not too bad. They would answer the survey more optimistically, as if this makes the issues go away. It takes a good capacity of self reflection to see the problems clearly, and the loss of such capacity often accompanies other mental health problems.
Additionally, it takes a particularly trusing personality to discuss your health issues in a web survey. You never know how anonymous it all really is and where the collected data may end up eventually. I'm not sure how this correlates with mental health. The paranoid types will obviously be less trusting, but I guess a certain level of care when sharing your personal health data should be normal. In any case, this is another inevitable source of bias in survey-based data.
These points don't invalidate the study, just suggest that it probably underestimates the real prevalence of mental health issues.
I would suggest it's possible that it overestimates things - online discussions of graduate school - on here, on Twitter, on Academia StackExchange, etc. have, in my experience, been oriented toward discussing negative experiences.
> The mental health of the remaining 1963 students who did not take the survey is very likely to be in worse shape than of those who did.
In discussion the authors say "Moreover, we want to emphasize the likely sample bias in our data. We recruited participants mainly via mailing lists and our project therefore probably has especially appealed to people who are already interested in health or aware of mental health issues."
I would counter that it may go in the other direction too. The other group of people who have little interest in the topic of mental health are those who are already doing really well. It's a non-problem for them, so why would they engage?
There is a dark side to this advice. Try calling yourself a thinker, a visionary, an ideas guy, a philosopher. Soon you start believing it, then it gets to your head and inflates your ego (already gigantic to begin with). And now your peers (or god forbid subordinates) are on a whole new level of misery when they have to deal with you.
Someone should submit a series of "boring numbers" to the OEIS. It would include all numbers not listed in any other series. Although it would be hard keeping it up-to-date.
+1 to FILCO, just want to add: Pick one with the letters printed on the sides of keycaps, not on top. This way they last longer. (BTW, my favorite switches are black, then red, I hate browns).
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