Analysis of an Experiment with Two-Level Factors - Design Tab

Analyzing the Results of a 2(k-p) Experiment

Select the Design tab in the Analysis of an Experiment with Two-Level Factors dialog box to access the options described here. Note that these results are for the currently specified model. You can specify a new model on the Model tab.

Display design and observed means

Click this button to produce a spreadsheet showing the unique runs (those with unique combinations of factor settings) in the experiment. In addition, for each unique run, Statistica will compute the mean, standard deviation, and standard error of the mean (if there is more than one run for the respective unique combination of factor settings).

Show text labels instead of factor values

When the Show text labels instead of factor values check box is selected, the factor settings in the spreadsheet will be identified by their respective text labels. If there are no text labels in the file (for the list of independent variables or factors), this option will not be available. Note that the setting of this option also determines whether text labels will be shown in square and cube plots, in spreadsheets with marginal means, and in marginal means plots.

Review factor names and settings

Click this button to produce a spreadsheet containing the factor names and the values of the low and high settings.

Generators of fractional design

As discussed in the general introduction to 2(k-p) designs (see the Introductory Overview), in fractional factorial designs, some factors are created as aliases of higher-order interactions. These higher-order interactions are commonly referred to as design generators. Click the Generators of fractional design button to view these interactions. Note that this option is only available if 1) the current design is a standard design, as generated by the Experimental Design module, and 2) if the current design is a fractional factorial design.

Generators of blocking var

As discussed in the general introduction of 2(k-p) designs (see the Introductory Overview), blocking is introduced into the design as an additional orthogonal factor. This requires assigning higher-order interactions to this factor (or two factors, if 4 blocks are requested; or three factors, if 8 blocks are requested, etc.). Thus, the blocking factors in those designs are the aliases of higher-order interactions. Click the Generators of blocking var button to view the generators (aliases) of the blocking factors. Note that this option is only available 1) if the current design is a standard design, as generated by the Experimental Design module, and 2) if there is a blocking variable in the design.

Aliases of effects

In fractional factorial designs, higher-order interactions are "sacrificed" in order to accommodate additional factors (main effects). Click the Aliases of effects button to view the aliases of main effects and interactions, that is, to examine the confounding of main effects with interactions, and of two-way interactions with higher-order interactions. The issue of confounding in 2(k-p) designs and the concept of resolution are explained in the Introductory Overview. Note that this option is only available if the current design is a standard design, as generated by the Experimental Design module.

Correlations

Use the options in the Correlations group box to review correlations for the design matrix as well as the effects.

Corr. matrix of design variables (X'X).

Click this button to produce a correlation matrix for the columns of the current design matrix. Thus, the number of effects displayed in this matrix depends on the current choice of the model in the Include in model group box on the Model tab. For analysis purposes, the factor values are recoded so that the range of values for each factor is ±1 (see also option Summary: Effect estimates on the Quick tab or the ANOVA/Effects tab). The interaction effects are then obtained by multiplying out the respective main effect vectors or columns. The correlations in this matrix, therefore, reflect on the redundancy of the respective effects. If, for example, an interaction column in the design matrix is correlated at 1.0 with another interaction column, then the two effects are completely confounded, i.e., they are aliases. To aid in the review of this matrix, all correlations that are not equal to 0.0 will be highlighted in this matrix.

Correlation of effects (X'X inverse)

Click this button to produce the standardized inverse of the correlation matrix (see above). This matrix can be interpreted as the correlation matrix of effects, that is, it is the standardized variance/covariance matrix of the parameter estimates for the current model. The greater the absolute value of a correlation between effects in this matrix, the more redundant are the respective effects. To aid in the review of this matrix, all correlations that are not equal to 0.0 will be highlighted in this matrix. Also, note that option Display matrices in compressed format (see below) applies to this option as well.

Display matrices in compressed format

When this check box is selected, the width of the columns in the spreadsheet with the correlations are set to 4 (4 characters, including the decimal point, will show in each cell of the correlation matrix, e.g., value 0.31). Use this compressed format to review large matrices efficiently. Clear this check box to display the cells in the spreadsheet in the usual default width of 8 characters per cell (e.g., to display 0.312345). Of course, you can always use the standard spreadsheet option Format - Cells to change the display format for all spreadsheets; (remember that, regardless of display format, values in spreadsheets are always stored in their highest precision).