You asked us anything–here’s our latest answer!
What “nuts and bolts” methods and data analysis techniques should every ecologist be familiar with, no matter what their job? (Matt Ricketts)
Brian: At the top of the list have to be ANOVA, regression and Principal Component Analysis – I would think it would be hard to read very far without understanding these. Beyond, that I think I would prioritize a deeper understanding of these. What are the assumptions of regression? How important are the violations? What can regression tell us and not tell us?
Beyond that generalized linear models (e.g., Poisson and logistic regression) is really important these days as are mixed models/random effects (the old fashioned linear regression context, not necessarily the Bayesian). Again deeper understanding is important – getting to know the Bayesian vs Monte Carlo vs likelihood approaches to these techniques is worth the time.
As far as newer stuff, I always say the three most underutilized statistical methods in ecology are regression trees (and more generally machine learning), path analysis and quantile regression. These are not just elaborations and improvements on the core linear regression (as everything in my last paragraph was), but fundamentally different ways to approach scientific inference.
Jeremy: More or less what Brian said: general linear models (which subsumes linear regression, multiple regression, ANOVA, ANCOVA, and combinations thereof as special cases) is the big one. Then generalized linear models and the simplest dimensionality reduction techniques like PCA. Then maybe randomization tests and bootstrapping, and the simplest model selection/guarding-against-overfitting techniques: AIC and cross validation. Beyond that, I think it’s very much need- and preference-specific. Brian cites path analysis, regression trees, and quantile regression, but I’ve never had the least need for any of those things in my own work, am not nearly as enthusiastic about them as Brian is, and haven’t even needed to know much about them to read the work of others. Much more useful to me has been time series analysis techniques (both time domain and frequency domain).