Workspace Node: GLZ Custom Design - Results - Means Tab

In the GLZ Custom Design node dialog box, under the Results heading, select the Means tab to access options to produce the means for any effect containing categorical predictor variables. If there are no categorical effects, these options are not available.

Note: results for stepwise or best-subset regression. Unlike in the stepwise or best-subset results in General Regression Models (GRM), the results produced from this tab always pertain to the full model, regardless of which effects were selected for inclusion during the model building procedure. The reason for this is that, unlike in GRM, the relationship between predictors, and their interactive effects (e.g., two predictors masking the effects of a third) are often much more complex. Also, unlike in GRM, because of the manner in which the p1, enter and p2, remove probabilities are determined [in forward stepwise selection, the score statistic is used to select new (significant) effects; while the Wald statistic is used during backward steps], the Forward stepwise and Backward stepwise methods may result in the repetitive selection and removal of one or more predictors. Therefore, the stepwise results can be reviewed separately, via the Model building button on the Summary tab.
Element Name Description
Effect Select the desired effect, and then specify to produce either the Observed unweighted, Observed weighted, or Predicted means. You can also display the means (unweighted, weighted, or predicted) for all categorical effects by clicking the respective All marginal tables ... buttons.
Observed unweighted Select this check box to produce a spreadsheet of the observed unweighted means. These are computed by averaging the means across the levels and combinations of levels of the factors not used in the marginal means table (or plot), and then dividing by the number of means in the average. Thus, each mean that is averaged to compute a marginal mean is implicitly assigned the same weight, regardless of the number of observations on which the respective mean is based. The resulting estimate is an unbiased estimate of m-bar (mu-bar), the population marginal mean. If the design is not balanced, and some means are based on different numbers of observations, then you can also compute the weighted marginal means (weighted by the respective cell N's). Note that the weighted mean is an unbiased estimate of the weighted population marginal mean (for details, see, for example, Milliken and Johnson, 1984, page 132).
Plot Select this check box to produce a graph of the observed unweighted means.
All marginal tables, observed unweighted Select this check box to produce the observed unweighted means for all categorical effects.
Observed weighted Select this check box to produce a spreadsheet of the observed weighted means. These are computed as the standard means for the respective combinations of factor levels, directly from the data. Thus, the resulting means are weighted marginal means, since they are weighted by the number of observations in each cell of the design (in full factorial designs, one could also compute the weighted marginal means by averaging the cell means involved in each marginal mean, weighted by the respective number of observations in the respective cells). Note that the weighted mean is an unbiased estimate of the weighted population marginal mean (for details, see, for example, Milliken and Johnson, 1984, page 132).
Plot Select this check box to produce a graph of the observed weighted means.
All marginal tables, observed weighted Select this check box to produce the observed unweighted means for all categorical effects.
Predicted Select this check box to produce a spreadsheet of the predicted means.
Plot Select this check box to produce a graph of the predicted means.
All marginal tables, predicted Select this check box to produce the predicted means for all categorical effects.
User-defined covariate values Select this check box to specify user-defined values for the continuous predictor variables (covariates) that will be used to compute the predicted means. After selecting this check box, click the adjacent button to display the Select factor/covariate values dialog box and specify the values.
Show standard errors Select this check box to display standard errors and confidence limits for the means in the spreadsheet or plot of means (see the above buttons). The plot of means will show the confidence limits as error bars around the respective means. The actual confidence limits are based on the current setting in the Conf. limit field available on the Summary tab.
Note: standard errors for unweighted marginal means. The standard errors for the observed unweighted means are computed based on the current error term from the ANOVA table:

Std.Err.(m-bar) = sest / t * sqrt[S(1/ni)]

In this formula, sest is the estimated sigma (computed as the square root of the estimated error variance from the current ANOVA table), t is the number of means that is averaged to compute the respective marginal mean, and ni refers to the number of observations in the t experimental conditions from which the respective unweighted marginal mean is computed.

Note: standard errors for weighted marginal means. The standard errors for the marginal means are computed as if you had ignored the other factors (those not in the marginal means table). Thus, for weighted marginal means the standard error is not dependent on the estimate of the error variance from the current ANOVA table, and hence, it is not dependent on the current model that is being fit to the data.
Conf. lev Type in the confidence level for the confidence interval calculation.

Stacked hist. Select this check box to produce a stacked histogram.

Options / C / W. See Common Options.

OK Click this button to accept all the specifications made in the dialog box and to close it. The analysis results are placed in the Reporting Documents node after running (updating) the project.