Method table for Fit General Linear Model

Find definitions and interpretation guidance for every statistic in the Method table.

Factor information

The factor information table displays the factors in the design, the type of factors, the number of levels, and the values of the levels.

Factors are the variables that you control in the experiment. Factors are also known as independent variables, explanatory variables, and predictor variables. Factors can assume only a limited number of possible values, known as factor levels. Factors can take text or numeric values. Numeric factors use a few controlled values in the experiment, even though many values are possible.

Interpretation

Use the factor information table to verify that you performed the analysis as you intended.

In a general linear model, factors can be either fixed or random. In general, if the investigator controls the levels of a factor, the factor is fixed. On the other hand, if the investigator randomly sampled the levels of a factor from a population, the factor is random.

For example, a quality analyst plans to study factors that could affect plastic strength during the manufacturing process. The analyst includes Additive, Temperature, and Operator in the experiment. The additive is a categorical variable which can be type A or type B. Temperature is a continuous variable but the analyst plans to include only three temperatures settings in the experiment: 100 °C, 150 °C, and 200 °C. Because the analyst controls the levels of these two factors in the experiment, these factors are both fixed. On the other hand, the analyst decides to randomly select operators from the plant population. Therefore, Operator is a random factor.

Factor Additive Temperature Operator
Type Fixed Fixed Random
Level A Low (100 °C) A
Level B Medium (150 °C) B
Level   High (200 °C) C

Factors can be crossed or nested. Two factors are crossed when each level of one factor occurs in combination with each level of the other factor. Two factors are nested when the levels of one factor are similar but not identical, and each occurs in combination with different levels of another factor.

For example, if a design contains machine and operator, these factors are crossed if all operators use all machines. However, operator is nested in machine if each machine has a different set of operators.

In the factor information table, parenthesis indicates nested factors. For example, Operator (Machine) indicates that operator is nested within machine.

For more information on factors, go to Factors and factor levels, What are factors, crossed factors, and nested factors?, and What is the difference between fixed and random factors?.

Factor coding

Minitab can use either the (0, 1) or (−1, 0, +1) coding scheme to include categorical variables in the model. The (0, 1) scheme is the default for regression analysis while the (−1, 0, +1) scheme is the default for ANOVA and DOE. The choice between these two schemes does not change the statistical significance of the categorical variables. However, the coding scheme does change the coefficients and how to interpret them.

Interpretation

Verify the coding scheme that is displayed to ensure that you performed the intended analysis. Interpret the coefficients for the categorical variables as follows:

  • With the (0, 1) coding scheme, each coefficient represents the difference between each level mean and the reference level mean. The coefficient for the reference level is not displayed in the Coefficients table.
  • With the (−1, 0,+1) coding scheme, each coefficient represents the difference between each level mean and the overall mean.

Covariate standardization

If you chose to standardize the covariates in your model, Minitab provides details about the method in the Covariate standardization table.

Usually, you use standardization to center variables, to scale variables, or both. When you center variables, you reduce multicollinearity caused by polynomial terms and interaction terms, which improves the precision of the coefficient estimates. In most cases, when you scale variables, Minitab converts the different scales of the variables to a common scale, which lets you compare the size of the coefficients.

Interpretation

Use the standardization method table to verify that you performed the analysis as you intended. Depending on your choice for the method, you may have to change the interpretation of the coefficients as follows:
Specify low and high levels to code as -1 and +1
This method both centers and scales the variables. Minitab uses this method in design of experiments (DOE). The coefficients represent the mean change in the response associated with the high and low values that you specified.
Subtract the mean, then divide by the standard deviation
This method both centers and scales the variables. Each coefficient represents the expected change in the response given a change of one standard deviation in the variable.
Subtract the mean
This method centers the variables. Each coefficient represents the expected change in the response given a one unit change in the variable, using the original measurement scale. When you subtract the mean, the constant coefficient is estimating the mean response when all the predictors are at their mean values.
Divide by the standard deviation
This method scales the variables. Each coefficient represents the expected change in the response given a change of one standard deviation in the variable.
Subtract a specified value, then divide by another
The effect and interpretation of this method depends on the values that you enter.

Estimated λ

When you use a Box-Cox transformation, the estimated λ (lambda) is the optimal value to produce transformed response values that are normally distributed. By default, Minitab uses the rounded lambda value.

Interpretation

Lambda is the exponent that Minitab uses to transform the response data. For example, if lambda = -1, then all response values (Y) are transformed as follows: −Y-1 = −1/Y. If lambda equals 0, this represents the natural log of Y rather than Y0.

95% CI for λ

The confidence intervals for λ (lambda) are ranges of values that are likely to contain the true value of λ for the entire population from which your sample was drawn.

Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. However, if you take many random samples, a certain percentage of the resulting confidence intervals contain the unknown population parameter. The percentage of these confidence intervals that contain the parameter is the confidence level of the interval.

Interpretation

Use the confidence interval to assess the estimate of lambda for your sample.

For example, with a 95% confidence level, you can be 95% confident that the confidence interval contains the value of lambda for the population. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

Rounded λ

By default, Minitab rounds the optimal λ (lambda) to the nearest half because these values correspond to a more intuitive transformation. If you want to use the optimal value for the transformation, choose Tools > Options > Linear Models > Display of Results.

Interpretation

The following are common rounded values of lambda and how they transform the response variable.
Lambda Transformation
-2 −Y-2 = −1 / Y2
-1 −Y-1 = −1 / Y
-0.5 −Y-0.5 = −1 / (square root of Y)
0 log (Y)
0.5 Y0.5 = square root of Y
1 Y
2 Y2
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