Hello
When is orthogonal blocking possible? Only when run size is a multiple of number of levels?
You are correct. It is not possible to make an orthogonal design with two-level factors in blocks of three runs.
@Mark_Bailey Thank you for your reply! I suppose that this also applies to the two-factor interaction effects?
Can you maybe give a short explanation on why this is not possible?
You cannot estimate the main effects and two-factor interaction effects with 48 runs. It will take at least 80 runs. The model matrix for the regression analysis will have 80 columns, so you need at least 80 rows for the ordinary least squares solution to the normal equations.
The question about orthogonality applies to any pair of the terms in the model. The answer is the 'inner product' or 'dot product' of the corresponding columns in the model matrix X that is used in regression to estimate the parameters must be zero. Regression analysis and solution of the normal equations does not require these columns to be orthogonal.
