Workspace Node: GLM Custom Design - Results - Means Tab

In the GLM Custom Design node dialog box, under the Results heading, select the Means tab to access options to display the means for any effect containing categorical predictor variables only, or for repeated measures effects. If there are no categorical effects or repeated measures effects in the model, this tab is not available. Select the check boxes for the statistics and/or graphs to be produced and placed in the Reporting Documents after running (updating) the project.

Element Name Description
Effect Select the desired effect in the Effect drop-down list, and then select to display or plot either the Observed, unweighted; Observed, weighted; or Least squares means. You can also display the means (unweighted, weighted, or least squares) for all categorical effects by clicking the respective All marginal tables buttons (see below).
Observed, unweighted Select this check box to produce a spreadsheet of the observed unweighted means for the selected Effect. 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 Ns). 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), and the standard errors for these means are estimated from the pooled within-cell variances.
Plot Select this check box to create a graph of the observed unweighted means for the selected Effect.
Select plot var Click this button to display a variable selection dialog box, where you specify the dependent variables to use in the means plot.
All marginal tables, observed unweighted Select this check box to produce spreadsheets of the observed unweighted means for all of the categorical effects (regardless of the Effect selected).
Observed, weighted Select this check box to produce a spreadsheet of the observed weighted means for the selected Effect. 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, you 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), and the standard errors for these means are estimated from the respective cell variances for each respective mean (i.e., the respective actual observed standard deviations in each cell).
Plot Select this check box to create a graph of the observed weighted means for the selected Effect.
Select plot var Click this button to display a variable selection dialog box, where you specify the dependent variables to use in the means plot.
All marginal tables, observed weighted Select this check box to produce spreadsheets of the observed weighted means for all of the categorical effects (regardless of the Effect selected).
Least squares means Select this check box to produce a spreadsheet of the least squares means for the selected Effect. Least squares means are the expected population marginal means, given the current model. Note that for full factorial designs without missing cells, the Least squares means are identical to the Observed, unweighted means (see above). Least squares means are also sometimes called predicted means, because they are the predicted values when all factors in the model are either held at their means or the factor levels for the respective means. Note that if there are continuous predictors (covariates) in the model, the least squares means are computed from the values for those predictors as set in the Covariate values group box (see below). For details concerning the computation of least squares means refer to Milliken and Johnson (1992), Searle, Speed, and Milliken (1980), or Searle (1987).
Plot Select this check box to create a graph of the least squares means for the selected Effect.
Select plot var Click this button to display a variable selection dialog box, where you specify the dependent variables to use in the means plot.
All marginal tables, least squares means Select this check box to produce spreadsheets of the least squares means for all of the categorical effects (regardless of the Effect selected).
Covariate values The options in this group box determine at what values the continuous predictor variables (covariates) will be set for the computation of least squares means. By default, the values for any continuous predictors (covariates) in the model will be held at their respective overall Covariate means.

You can also specify User-defined values for the covariates; after selecting this option button, click the Define button to display the Select factor/covariate values dialog box and specify the values.

Finally, you can set the values for the continuous predictor variables so as to compute the Adjusted means, these are the predicted values (means) after "adjusting" for the variation of the means of the continuous predictor variables over the cells in the current Effect. Adjusted means are widely discussed in the traditional analysis of covariance (ANCOVA) literature; see, for example, Finn (1974), Pedhazur (1973), or Winer, Brown, and Michels, K. M. (1991). The Adjusted means option button is only available in full factorial designs.

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. The plot of means will show the confidence limits as error bars around the respective means. The actual confidence limits are based on the setting in the Confidence limits field available on the GLM 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.
Show means +/- std errs Select this check box to show in the tables and plots of means the plus or minus standard error range around each mean. These will only be shown if the Show standard errors check box is also selected. By default, when the Show means +/- std errs check box is cleared, the (95%) confidence intervals will be computed instead (or any other confidence interval, consistent with the specification in the Confidence limits field of the Results - Summary tab).

Options / C / W. See Common Options.

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