GLZ Results - Means Tab

Select the Means tab of the GLZ Results dialog box to access options to display 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. (See GLZ Quick Specs - Advanced tab for further details on the Stepwise and p options.) Therefore, the stepwise results can be reviewed separately in this dialog, via the Model building button on the GLZ Results - Summary tab. If, after comparing the overall model (with all effects) with the one suggested by the model building procedure, you decide to further evaluate the latter model, use option Make model on the GLZ Results - Summary tab to transfer that model to the GLZ Quick Specs or GLZ Analysis Syntax Editor, and then fit that model to the data.

Effect. Select the desired effect in the Effect box, then select to display or plot 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. Click the Observed, unweighted button to display 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. Click the Plot button to display a graph of the observed unweighted means. Depending upon your design, when you click this button, the Specify the Arrangement of the Factors in the Plot dialog box may be displayed, which is used to specify the arrangement of factors that STATISTICA will use in the means plot.

All marginal tables, observed unweighted. Click the All marginal tables, observed unweighted button to display the observed unweighted means for all categorical effects.

Observed, weighted. Click the Observed, weighted button to display 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. Click the Plot button to display a graph of the observed weighted means. Depending upon your design, when you click this button, the Specify the Arrangement of the Factors in the Plot dialog box may be displayed, which is used to specify the arrangement of factors that STATISTICA will use in the means plot.

All marginal tables, observed weighted. Click the All marginal tables, observed weighted button to display the observed unweighted means for all categorical effects.

Predicted. Click the Predicted button to display a spreadsheet of the predicted means. The predicted means are equivalent to the Least squares means option described in the GLM, GRM, and ANOVA Results - Means tab topic. Hence, predicted means are the expected values for the respective nonlinear (generalized linear) model.

Plot. Click the Plot button to display a graph of the predicted means. Depending upon your design, when you click this button, the Specify the Arrangement of the Factors in the Plot dialog box may be displayed, which is used to specify the arrangement of factors that STATISTICA will use in the means plot.

All marginal tables, predicted. Click the All marginal tables, predicted button to display the predicted means for all categorical effects.

User-defined covariate values. Select the User-defined covariate values 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 button to display the Values for Covariates dialog box and specify the values.

Show standard errors. Select the Show standard errors 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 GLZ Results - 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. Specify the confidence level here.

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

See also, GLZ - Index.