For designed experiments, if blocks are orthogonal to the other effects in the design matrix, then Response Optimizer (and contour plot) uses the average of the block effect to calculate the fit. This is analogous to using the fits when blocks are not included in the model.

If the blocks are not orthogonal to the other terms in the design matrix, the Response Optimizer (and contour plot) uses the coefficients from the model with the block term included, but the coefficient from the block term is dropped. Minitab drops the coefficient because it assumes the blocking factor is a random or environmental factor you cannot control, and thus, do not want to specify when predicting the response.

If the blocks are orthogonal to the other effects in the design matrix, the coefficients do not change when you include the block term in the model. However, including blocks in the model adds one more coefficient, which causes the fits to change. If the blocks are not orthogonal to the other effects, the coefficients change when you include the block term in the model.

Blocks are coded for factorial and response surface analyses. For example, with 2 blocks, the block column in the worksheet contains 1s and 2s. However, the block column is analyzed with 1s and -1s (the block column in the design matrix).