# Specify the options for Analyze Variability

Stat > DOE > Factorial > Analyze Variability > Options

## Estimation method

In Estimation method, choose between the least squares estimation (LSE) and maximum likelihood estimation (MLE) methods. The methods produce equivalent estimates of the coefficients in the saturated model, when the number of parameters equals the number of data points.

Often, the differences between the LSE and MLE results are minor, and the methods can be used interchangeably. You might want to use both methods and determine whether the results confirm each other. If the results differ, you might want to determine why. For example, MLE assumes that the original data are from a normal distribution. If your data might not be normally distributed, LSE may provide better estimates. Also, LSE cannot calculate results for data that contain a standard deviation equal to zero. MLE might provide estimates, depending on the model.

You can use LSE and MLE together because LSE provides better p-values, while MLE provides more precise coefficients1. To use this approach, follow these steps:
1. Use the p-values from the LSE to determine which terms are statistically significant.
2. Fit the model again, excluding nonsignificant terms to identify the appropriate reduced model.
3. Use MLE to estimate the final coefficients of the model and to determine the fits and the residuals.

## Confidence level for all intervals

Enter the level of confidence for the confidence intervals for the coefficients and the fitted values.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you took 100 random samples from the population, the confidence intervals for approximately 95 of the samples would contain the mean response. For a given set of data, a lower confidence level produces a narrower interval, and a higher confidence level produces a wider interval.

###### Note

To display the confidence intervals, you must go to the Results sub-dialog box, and from Display of results, select Expanded tables.

## Type of confidence interval

Select the type of confidence interval or bound that you want to display.

For example, the predicted mean concentration of dissolved solids in water is 13.2 mg/L. The 95% confidence interval for the mean of multiple future observations is 12.8 mg/L to 13.6 mg/L. The 95% upper bound for the mean of multiple future observations is 13.5 mg/L, which is more precise because the bound is closer to the predicted mean.
• Two-sided: Use a two-sided confidence interval to estimate both likely lower and upper values for the mean response.
• Lower bound: Use a lower bound to estimate a likely lower value for the mean response.
• Upper bound: Use an upper confidence bound to estimate a likely higher value for the mean response.

## Means table

You can display the means for the main effects, the main effects and two-way interactions, or all terms in the model in the output. Alternatively, you can display the means for a subset of these terms, or no terms.

If you select Specified terms, use the arrow buttons to move terms from one list to the other. Available Terms shows all the terms that you can display means for. Minitab displays the means for the terms in Selected Terms. Select one or more terms in one of the lists, then click an arrow button. The double arrows move all the terms in one list to the other. You can also move a term by double-clicking it. If a term you expected to see in the list does not appear, you need to add it to the model.

1 Nair, V.N., and Pregibon, D. (1988). "Analyzing Dispersion Effects From Replicated Factorial Experiments," Technometrics, 30, pp.247-257.
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