# Variance Estimation and Precision Results - Means Comparisons Tab

Select the Means Comparisons tab of the Variance Estimation and Precision Results dialog box to access the options described here.

Note about LS Means. Least squares means and their standard errors are computed from the solutions to the mixed model equations. The statistical significance of individual mean comparisons may not always be consistent with the ANOVA results which are computed from the expected mean squares. Using the default REML method will ensure consistency of p-values. For more information on the two estimation methods, see ANOVA and REML Method Implementation in Variance Estimation and Precision.

Variability plot. Click the Variability plot button to display a variability plot for each of the selected response variable(s). This type of graph is useful to evaluate the variability of one factor within several other organizing factors. Options for customizing the default variability plot (e.g., putting boxes around organizing factors or showing group means/medians) are available by double-clicking in the graph background and selecting the Plot: Variability Plot tab of the Graph Options dialog box. If there are more than seven factors in the design, you will be prompted to select the (up to seven) factors to use in the variability plot. Initially, selected factors are plotted using the order found in the spreadsheet (e.g., Var1, Var2, Var3, etc.). Options for rearranging factor order and adding a replicate factor are available in the Plot: Variability Plot tab of the Graph Options dialog box.

ANOVA table. Click the ANOVA table button to display a spreadsheet(s) containing univariate results for the selected response variable(s). When the ANOVA estimation method has been selected (see Estimation method on the Define/Review Model dialog box), results are given for each effect and include degrees of freedom and mean squares, denominator synthesis degrees of freedom and mean squares, F test-statistic and p-value. For more information on denominator synthesis and how results are calculated for each estimating method, see Computational Details. See also, ANOVA and REML Implementation.

Previewing the ANOVA table. If you have not specified a response variable (or if you have not yet collected data for your response variables), you can click the ANOVA table button to display a minimal ANOVA table that indicates the degrees of freedom associated with each (combined) effect. Items in this "skeleton" ANOVA table are color coded based on their degrees of freedom. Combined effects with fewer than 4 degrees of freedom are displayed in red, combined effects with 4-8 degrees of freedom are shown in yellow, and combined effects with more than 8 degrees of freedom are shown in green. A warning will also be displayed for any fixed, interaction effects that have empty cells in the design.

Descriptive statistics. Click the Descriptive statistics button to display a spreadsheet of descriptive statistics for the different factor levels. Statistics in the spreadsheet include sample size, means, standard deviations, standard errors, and confidence limits. Empty cells in the design are not displayed. Enter the confidence level in the Alpha for confidence interval group box.

Observed means with SE. Click the Observed means with SE button to display the Select an effect dialog box, that lists the estimable effects for which observed means can be calculated. Once you select an effect, a spreadsheet and plot of the observed (weighted) means will be displayed. If more than one response variable is selected in the Response list box, the selected effect will be used for all plots.

LS means with SE. Click the LS means with SE button to display the Select an effect dialog box that lists the estimable effects for which least square means can be calculated. Once you select an effect, a spreadsheet and plot of the least squares means with plus/minus one standard error will be displayed. Least squares means are the expected population marginal means, given the current model. Thus, these are usually the means of interest when interpreting significant effects from the ANOVA table. Note that for full factorial designs without missing cells, the least squares means are identical to the observed, unweighted means. 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 for the means of the covariates. For details concerning the computation of least squares means refer to Milliken and Johnson (1992), Searle, Speed, and Milliken (1980), or Searle (1987). If more than one response variable is selected in the Response list box, the selected effect will be used for all plots.

LS means with CI. Click the LS means with CI button to display the Select an effect dialog box that lists the estimable effects for which least square means can be calculated. Once you select an effect, a spreadsheet and plot of the least squares means with 95% confidence limits [or the confidence limits specified in Alpha for confidence interval (see below)] will be displayed. See LS means with SE (above) for more information on least squares means. If more than one response variable is selected in the Response list box, the selected effect will be used for all plots.

Pairwise comparisons, LS means. Click the Pairwise comparisons of LS means button to display the Select an effect dialog box that lists the estimable effects for which least square means can be calculated. Once you have selected an effect, spreadsheets containing between contrast coefficients, contrast estimates, and the univariate test of significance for planned comparisons will be displayed.

Alpha for confidence interval. Use the Alpha for confidence interval group box to specify confidence limits. These values are used in all results spreadsheets and graphs whenever a confidence limit is to be computed.