# Analyze location effects and dispersion effects

Minitab lets you analyze both location and dispersion effects in a 2-level factorial design. To examine dispersion effects, you must have either repeat or replicate measurements of your response.
Location model
Examines the relationship between the mean of the response and the factors.
Dispersion model
Examines the relationship between the standard deviation of the repeat or replicate responses and the factors.

When you have determined your design and collected data, you can analyze both location and dispersion models. The following is a list of steps for analyzing location and dispersion models in Minitab, with options to consider at each step:

1. Calculate or define standard deviations of repeat or replicate responses with Pre-Process Responses for Analyze Variability. To open Pre-Process Responses for Analyze Variability, choose Stat > DOE > Factorial > Pre-Process Responses for Analyze Variability.
2. Analyze dispersion model with Analyze Variability. To open Analyze Variability, choose Stat > DOE > Factorial > Analyze Variability.
Consider whether to:
• Use least squares or maximum likelihood estimation methods, or both.
• Store weights, using fitted or adjusted variance, to use when analyzing the location model.
3. Analyze location model with Analyze Factorial Design. To open Analyze Factorial Design, choose Stat > DOE > Factorial > Analyze Factorial Design.
Consider:
• Which response column to use:
• If you have repeats, use the column of stored means calculated in Preprocess Responses.
• If you have replicates, use the column containing the original response data.

For example, a 23 factorial design with four repeats has eight experimental runs with four measurements per run. Minitab calculates the mean of the four repeats at each run, giving you a total of eight observations. The same design with four replicates has 32 experimental runs. In this case, each measurement is a distinct observation, giving you 32 observations. Experiments with replicate measurements have more degrees of freedom for the error term than experiments with repeats, which provide greater power to determine differences between factor settings in the location model.

• Whether to use weights stored in the dispersion analysis.
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