I have been asked to propose a course in experimental design for advanced graduate students in agronomy and ecology. I have never taken such a course, and was surprised to find that the course might be more aptly named "Beyond one-way ANOVA", and that it covers material that I learned in an advanced graduate course on statistics for agricultural field experiments (e.g. RCBD, Latin Squares, Contrasts, repeated measurements, and covariates). Perhaps I am confused by the name "Experimental Design" rather than "Analysis of Experimental Results".
I have some ideas about what such a course should contain and would appreciate feedback on how this might be integrated into a statistics curriculum that meets the needs of the students while presenting modern alternatives to named lists of designs and their associated tests.
For example, I can't imagine teaching students to use linear and quadratic contrasts with ANOVA that enforces categorization of continuous variables when I could teach them to compare regression models with linear and quadratic functions. In the second case, they would also learn how to deal with factors that are not experimentally defined discrete values. If anything, I might compare the two approaches.
If I were to teach a course in "Experimental Design" I would really like to emphasize fundamental concepts that are independent of the statistical model being applied, and that would translate more broadly to other problems. This would enable students more flexibility to use modern statistical approaches.
Some of the relevant concepts that do not appear to be covered in the existing course include:
- hierarchical and mixed models (of which I understand ANOVA and relatives as one example)
- model comparison (e.g. to replace contrasts)
- using spatial models instead of blocks as 'factors'
- replication, randomization, and IID
- differences among hypothesis testing, p-hacking, and pattern recognition.
- power analysis through simulation (e.g. recovery of parameters from simulated data sets),
- use of prior knowledge from published studies and scientific principles.
Are there any courses that currently take such an approach? Any texts books with such a focus?