- What does independence mean? Is it an assumption you have to verify? What changes when it is violated?
- Stationarity. As I undertand it, roughly it means the situation you are statistics-ing doesn't change (when relaxed: too much, too quickly). Basic statistics pretends you have this property. In many situations, it is clear that we don't and can't have it exactly. To what extent is this reasonable? What goes wrong when you don't have it? How can we make sense of statistics that talks about things like "true" parameters? What can we do about it? (I feel like I've written about this before and forgotten the details... maybe this is the key point for digital gardens over blogs.)
- To do statistics, you may have to answer "What counts as?" Any analysis is an implicit, nebulous, potentially inconsistent or incoherent answer to that question.
- How do we "force" our statistical models/tools to "work"? How do we make them fit the situation we are using them in? What does fit mean? What can make one model a better choice than another?
- How would you know if statistics was working or not in a given situation? When does it make sense to apply statistics at all?