I'm doing a biology course and am very inexperienced with stats. My supervisor recommended that I go away and try an ANOVA with block design, but I hadn't heard of this. Having looked up about it, I can't tell the difference between that and a nested ANOVA. Please could someone explain? I will be running it in R and have only ever done regular one-way ANOVAs, GLMs and ANCOVAs before, so I'd like to keep my analysis as simple as possible.
Here is my understanding of the difference. With a randomized block design, you have a characteristic of the units-of-analysis that you stratify (block) and then randomize into your treatment conditions within each block. For example, you could block on sex (male and female) and then randomly assign to a treatment and control condition separately for males and females, ensuring balance across the blocks in the number assigned to each group. In this design, you have one factor (treatment/control) and one block (male/female). This design also controls for any variance associated with the block (you would only want to use a block that you have good reason to believe is associated with the dependent variable)
In a nested design, you have two factors but rather than the factors being fully crossed, they are nested. An example from Snedecor and Cochran (1989) of a nested design has multiple samples taken from individual leaves, with three leaves per plant and four plants. In this design, you have two factors: plants and leaves, and the leaves are nested within the plants.
Statistically, the analysis of these designs is the same. The distinction, as far as I can tell, is either you are simply ensuring balance of a potential nuisance variable via blocking thru block-randomization or whether you simply have two nested factors.
The bottomline is that I don't think the distinction matters much. I'd be interested in what others think, however. The classic book by Kirk on ANOVA addresses both block-randomized and nested ANOVA designs, if I recall, but my copy is at the office and I am not.