A little while back we invited you to ask us anything. Here are the next questions, and our answers. Questions have been edited for clarity and brevity; see the comments on the linked post for the original questions.
What text/online resources do you recommend for self-teaching intro stats (up through ANOVA)? (from Peter, @onepintmore)
Jeremy: I teach intro biostats from Whitlock & Schluter. I like it a lot, and its flaws are shared by every intro biostats textbook of which I’m aware. For historical reasons, it has separate chapters on t-tests, regression, ANOVA, etc. I think it would be a big improvement, conceptually and pedagogically, to just teach general linear models from the start, noting in passing that for historical reasons, various special cases have their own names. But as far as I know, there’s no GLM-based biostats text written at the low level of Whitlock & Schluter, and with Whitlock & Schluter’s other virtues (e.g., tons of concrete examples and practice problems).
The free online resources of which I’m aware aren’t nearly as good. Sorry. For instance, many of the most popular YouTube videos on basic stats concepts contain serious mistakes. And based on an admittedly small and old sample, I find Wikipedia’s stats pages are very hit and miss (the one time I tried to edit Wikipedia, many years ago, it was to correct howlers in the page on the Mann-Whitney U test, a nonparametric test sometimes taught in intro biostats courses). I know of good free resources on specific topics, but nothing comprehensive. But it’s possible there are good free comprehensive resources out there that I’m not aware of.
Statistics Done Wrong is a good free website (and now a book, I believe) on common statistical mistakes, including some important ones that aren’t widely covered in introductory textbooks (e.g., researcher degrees of freedom, stopping rules, regression to the mean). Good for both students learning statistics, and people who just want to avoid common fallacies of quantitative reasoning in their everyday lives. It’s a good complement to a standard introductory stats textbook.
In terms of learning statistical software, if you’re an absolute beginner I recommend Petchey & Beckerman’s Getting Started with R. (full disclosure: the authors are friends of mine)
Brian: I guess it depend whether you’re talking undergrad or graduate. It’s been a long time since I taught undergraduate statistics, so I’m not sure I have a great recommendation. Beckerman & Petchey’s Getting Started with R and Zuur et al’s Beginner’s Guide to R are both very well written. They both have a pretty clear spin of introducing R, but they have a lot of good introductory statistics along the way, and really can you say you’re learning stats if you’re not learning R along the way these days? (and R is what will give most people the most grief so having a real well-done intro to R is probably a key success point anyway). For graduate students I’ve taught a lot of stats courses and used a lot of books. I have absolutely no hesitation saying that Gotelli & Ellison’s Primer of Statistics and Zuur et al’s Analysis of Ecological Data are by far the most clearly written, educational books out there. They both go further than ANOVA, but I still think they’re the best books even for people looking just to work up through ANOVA
What courses/books/papers/exercises/etc. would you recommend to early career ecologists with an applied orientation and limited mathematical chops who want to make use of theory in their work? And to what extent is the needed theoretical background subdiscipline-specific? (from Dunbar Carpenter)
Jeremy: I recommend Ted Case’s Illustrated Guide to Theoretical Ecology. I’ve taught undergrads from it for years. Does what it says on the tin, as the British say. Emphasizes graphs illustrating the math–e.g., plots of nonlinear functions, with handy little textboxes and arrows calling your attention to key features. Completely unlike any other intro theory textbook out there, and by far the best starting point for someone with little mathematical background.
After that, I’d recommend working your way through Otto & Day’s A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. Or else focusing on specific bits of math that are common in your subdiscipline.
Brian: my recommendation is exactly the same as Jeremy’s. Both superlative books. Beyond that, I would say start reading theory papers in the area of ecology you are interested in and really spend time understanding what they’re doing. Reread the equations 5 times. Look it up when you’re stuck. Ask for help when you’re stuck. There is no substitute for learning by example from others. Reading an intro book and then continuing to just skim the equations in the papers in your field is not going to get you anywhere. It will take a lot of time in the beginning but it will get faster if you are persistent. (Jeremy adds: Brian’s suggestion is great, I should’ve remembered to say it myself. That’s how I’ve learned most of the theory I know.)