Recommendations what to teach and what you should know at different levels in your studies (check the curriculum proposal for the of the American Statistical Association)
Level 1: Statistics 101 (BSc)
- Random variable, histograms, sample statistics (incl. median, IQR)
- distributions: estimates vs. statistics
- PDF, CDF; (mass function)
- likelihood, maximum likelihood
- correlation & X2-test
- GLM, regression
- Design of experiments & hypothesis testing philosophy
- ANOVA
- transformations and ranking; problem of ratios and percentages
- power (t-test, ANOVA)
- PCA, recursive partitioning (for clustering)
Level 2: Applied and Advanced Statistics (MSc, PhD)
- mixed models
- zero-inflation
- survival analysis (censored data, Cox-prop.hazard, Weibull-> Zucchini, GÖ)
- randomisation, bootstrap
- clustering (divisive, agglomerative), minimum spanning tree
- ordination (PCA, nMDS; RDA, PCoA) and permutation tests
- model selection, variance-bias trade-off, cross-validation
- optimisation, non-linear models
- CART, GAM
- prospective power by simulation
Level 3: Specific statistical topics (as separate or combined modules)
- Robust statistics & non-parametric statistics
- WinBUGS
- MCMC, from Metropolis to Gibbs & inverse modelling
- multivariate statistics: old school (CA/DCA, CCA) & cutting edge (tests, bioenv, …)
- time series analysis (detrending, autoregressive models, stl, spectral analysis, wavelets)
- geo- and spatial statistics
- ecological statistics (FD, SAR, richness, BDEF)
- ecological modelling (ODE, diff eq)
- scientific programming in R (for, if, vectorised, OOP, package building, docu)