You can calculate and store weights using fitted or adjusted variances based on dispersion model to use when analyzing the location model.
For the weights for replicates, which use the fitted variance, the weights are the reciprocal of the fitted variance:
For the weights for repeats, using the adjusted variance, the weights are the reciprocal of the fitted variance for the mean across repeats. The variance of the mean of repeats is:
- σ2(between) + σ2 (within) / number of repeats
"Between" and "within" refer to a run of the experiment. Variation within a run is what you measure with the standard deviation for repeat observations. Variation between runs refers to the additional sources of variation for new runs.
When you analyze the standard deviation across repeats, you are fitting a model to s (within). If you have replicates, Minitab combines the model for σ2 (within) and the variance of means across replicates to obtain an estimate of σ2 (between). Then, the estimate of σ2 (between) is recombined with σ2 (within) / number of repeats to get variance estimates for the means that are consistent with your dispersion model.
This approach assumes that σ2(between) is constant, and does not depend on the factor levels. If this assumption is incorrect, you may want to fit a model to the variance of x by using Preprocess responses with to get σ2 across replicates.
If you have covariates in your model, you should account for them in the variance for repeats. You cannot account for covariates in the fitted variance.