Experiment design: levels vs factors Experiment design: there are multiple ways to group factor levels. How do you "decide" the number of factors and levels in your experiment, i.e. whether a factor level is a level or a separate factor?
It appears that thinking in treatments (factor level combinations) removes that ambiguity.
 A: The ultimate decision depends on what you are interested in learning about. 
As an example, if you want to learn about the impact of a novel teaching method on students' scores for a particular subject matter, you would design a study where you would randomly assign students to one of two teaching methods: standard method or novel method.  At the end of the semester, you would measure their scores for that subject and compare the average scores across the two types of teaching methods.  In this case, the factor of interest is teaching method and it has two levels: standard method and novel method.
If you want to control for the effect of study time on students's scores when investigating the effect of teaching method on the same scores, you could further consider a second factor: study time.  This factor could have levels such as: small, moderate or high. Obviously, the more levels you allow for study time, the more you can "zoom in" on different student sub-populations so that you can make statements like these (if you had 3 levels, say): For students who spend a high amount of time studying, the novel teaching method is significantly better than the standard teaching method with respect to the average score. However, for students who spend low or moderate amounts of time studying, there is no evidence that the novel method is better than the standard method.  
In the context of this example, teaching method is bound to have only two levels. But study time can have 2 or more levels, depending on what student subpopulations you may be interested in. 
It takes a lot of thought sometimes to decide what factors are important to include in a study and how many levels they should each have.  The answers are not always straightforward.  If you include too many factors with too many levels, you may need a lot more data to detect the effects of interest than if you include fewer factors with fewer levels. So start small and build from there.
