Main Effects and Interactions for Experiments with Two-Level Factors
Both the Quick tab and the ANOVA/Effects tab of the Analysis of an Experiment with Two-Level Factors dialog box contain the Summary: Effect estimates button. Click this button to produce a spreadsheet with the ANOVA effect estimates and coefficients for the coded model. The effects that will be computed depend on the current model, as specified via the options in the Include in model group box on the Model tab. If an error term for the ANOVA is available, then this spreadsheet will also include the standard errors of the parameter estimates and coefficients, their confidence intervals, and their statistical significance.
All estimates in this spreadsheet pertain to the coded factor settings, that is, to the factor settings scaled to the ±1 range. To see the results for the original (untransformed) factor settings, click the Regression coefficients button on the ANOVA/Effects tab.
- Mean/Intercept
- The row labeled Mean/ Interc. contains the estimate of the intercept for the regression model, based the coded factor settings (see also Multiple Regression). If the design is balanced, and the factor effects are uncorrelated with the estimate of the mean, then the intercept value is the same as the overall mean for the respective variable.
- Block effects
- The block effects are computed from recoded added variables (to the design), one for each degree of freedom. For example, if you have 4 blocks in the design then 3 new variables are created to exploit the 3 degrees of freedom associated with the overall block effect. Specifically, each new variable bi is computed as:
- Curvature
- If a Curvature check is selected in the Include in model group box on the Model tab (only available if the design contains center points, see also Introductory Overview), a new variable will be added (to the design), and the effect estimate and coefficient for that variable reported in this spreadsheet. Specifically, the new variable C is computed as:
- Main effects
- The values shown in the column labeled Effect and in the rows labeled by the main effects are the ANOVA effect estimates. These can be interpreted as the differences (for the dependent variable) between the low settings and the high settings for the respective factors. The values shown in the column labeled Coeff. are the regression coefficients for the coded model, and they can be interpreted as the differences between the high factor settings and the averages of the low and high factor settings for the respective factors. Thus, they are half the size of the Effect estimates.
- Interaction effects
- The values in the Effect column, in the rows denoting the factor interaction effects, can be interpreted as follows: The two-way interaction effects can be interpreted as (see Mason, Gunst, and Hess, 1989, page 127) half the difference between the main effects of one factor at the two levels of a second factor; likewise, the three-way interaction effects can be interpreted as half the difference between the two-factor interaction effects at the two levels of a third factor, and so on. Again, the values in the Coeff. column are half the Effect estimates.
- Standard error of parameter estimates
- The standard errors for the parameter estimates (ANOVA estimates and coefficients) are computed from the current ANOVA error term, as selected in the ANOVA error term group box and depending on the model as specified in the Include in model group box, both on the Model tab.