How can I treat blocks in a split plot design?

Question

In a field experiment involving crops, what is the difference in considering block as random or otherwise as fixed factor? As far as I understood, random means that conclusion can be extended to other levels not included in the study; fixed factor on the contrary restricts the analysis only to a specific experiment.

Answer 1

The way you are thinking is one of the ways most people interpret blocks. But the bigger picture which sometimes people don't notice is: Blocks are a way to model a correlation structure. They let us "eliminate" or control for factors which we know influence the outcomes but are not really of interest. However, your conclusion about fixed factors may not be true in general. If the sampling is random and the effects can be considered fixed (or the individual variances are not very large), fixed factor analysis can be generalized to the population.

On a different note, if you read Casella's Statistical Design, he points out that blocks need not be treated as random. It does makes sense to treat them as random, but not all the time. In most of the cases, thinking about blocks as a tool to impose a correlation structure or control for the "unknown" factors helps.