Overview

The Model tab is where you specify which terms to include in your multifactor ANOVA model. The model determines which effects and interactions Prism will test in the analysis. You have control over which terms to include - main effects, two-way interactions, and three-way interactions can all be included or excluded based on your analytical needs.

Why model specification matters:

•Including more terms provides a more complete picture of how factors interact

•Each term consumes degrees of freedom and reduces power for detecting effects

•Interactions can be difficult to interpret, especially three-way interactions

Understanding the Model Hierarchy

The Model tab presents your model terms in a hierarchical structure:

Main effects test whether each factor, considered individually, affects the outcome. For example, if your factors are Treatment and Sex, the main effect of Treatment tests whether the average response differs across treatment groups (averaged over both sexes). The main effect of Sex tests whether males and females differ on average (averaged over all treatments).

Two-way interactions test whether the effect of one factor depends on the level of another factor. A Treatment:Sex interaction tests whether the treatment effect differs between males and females. If there's no interaction, the treatment effect is similar in both sexes. If there is an interaction, the treatment might work differently (or only work) in one sex.

Three-way interactions test whether a two-way interaction itself changes across levels of a third factor. For example, a Treatment:Sex:Age interaction would test whether the Treatment:Sex interaction differs between young and old subjects. These interactions are present when you have three or more factors and can be challenging to interpret.

Selecting Model Terms

The Model tab displays checkboxes for each type of term in your model:

•Main effects: This checkbox controls all main effect terms. When checked (the default), all individual factors are included in the model. When unchecked, no main effects are tested. You can expand this section to include or exclude individual factors.

•Two-way interactions: This checkbox serves as a master control for all two-way interactions. When checked, you can expand this section to see and select specific interactions individually. When unchecked, no two-way interactions are included.

•Three-way interactions: This checkbox controls all three-way interaction terms. When checked, all possible three-way interactions are included. This checkbox is only available when you have three or more factors in your design.

Expanding and Customizing Terms

Click the arrow next to "Main effects", "Two-way interactions", or "Three-way interactions" to expand that section and see the individual terms available. This allows you to selectively include or exclude specific terms rather than including all of them as a group.

Main effects: When expanded, shows each individual factor. Uncheck a factor to exclude it from the model.

Two-way interactions: When expanded, shows each factor with its own expandable section containing all two-way interactions involving that factor. You can uncheck an entire factor's branch to exclude all its two-way interactions, or expand the factor to selectively include/exclude specific interactions.

Three-way interactions: When expanded, shows each factor with its own expandable section containing expandable sections representing all combinations of two factors. When these sections are expanded, each corresponding three-way interaction is displayed.

Example: Suppose you have three factors - [A] Treatment, [B] Sex, and [C] Age. When you expand "Two-way interactions" and then expand "[B] Sex", you'll see:

•[B] Sex : [A] Treatment

•[B] Sex : [C] Age

You can include or exclude each of these interactions independently. Note that if you expand "[A] Treatment", you'll also see "[A] Treatment : [B] Sex" - this is the same interaction shown in a different location for convenience.

Removing Factors from the Model

There are two ways to completely remove a factor from your analysis:

Method 1: Unassign the variable on the Data tab

Return to the Data tab and remove the variable from the grouping variables panel. This automatically removes the factor and all its interactions from the model.

Method 2: Manually exclude on the Model tab

Expand "Main effects" and uncheck the factor you want to exclude, then manually uncheck all interactions involving that factor in the two-way and three-way interaction sections.

Important: When using Method 2, unchecking a main effect does not automatically remove that factor's interactions from the model. You must manually uncheck each interaction. However, you can efficiently remove all two-way interactions for a factor by unchecking that factor's branch in the "Two-way interactions" section rather than unchecking each interaction individually.

Model Formula Display

At the bottom of the Model tab, Prism displays the complete model formula. This formula shows your response variable (outcome) on the left side of a tilde (~), followed by all predictor terms separated by plus signs (+) on the right side.

Interaction terms are indicated with colons. For example:

Height ~ Treatment + Sex + Age + Treatment:Sex + Treatment:Age + Sex:Age

This formula tells you that Height is being modeled as a function of three main effects (Treatment, Sex, Age) plus three two-way interactions.

As you check or uncheck terms in the Model tab, watch the formula update in real-time to reflect your selections. This provides an immediate, compact view of your model specification.

Important Statistical Principles

The Hierarchical Principle

In most situations, if you include an interaction term in your model, you should also include all lower-order terms that compose it. This is called the hierarchical principle or marginality principle.

Example: If you include the Treatment:Sex interaction, you should generally include both the Treatment main effect and the Sex main effect. Similarly, if you include a Treatment:Sex:Age three-way interaction, you should include all three main effects and all three two-way interactions (Treatment:Sex, Treatment:Age, and Sex:Age).

Why this matters:

•Interaction terms are mathematically defined relative to main effects

•Excluding lower-order terms when interactions are present can lead to misleading results

•The interpretation of interaction coefficients depends on lower-order terms being in the model

•Violating hierarchy can make results difficult to interpret and reproduce

Important: Prism does not automatically enforce the hierarchical principle. It is your responsibility to ensure your model respects hierarchy if that's appropriate for your analysis. While most standard analyses should follow this principle, there are specialized cases (such as certain types of designed experiments or models with centered predictors) where non-hierarchical models may be appropriate.

Degrees of Freedom and Statistical Power

Each term you add to your model consumes degrees of freedom. With a fixed sample size, adding more terms means:

•Fewer degrees of freedom for the error term

•Less statistical power to detect effects

•Wider confidence intervals

•Less precise estimates

Rule of thumb: With small sample sizes (few observations per cell), consider limiting your model to main effects and key two-way interactions rather than including all possible terms. With large sample sizes, including all available terms (including three-way interactions) is more feasible.

Interpretation Complexity

Two-way interactions test whether "the effect of A depends on B" and are usually interpretable with careful examination. Three-way interactions test whether "the A:B interaction depends on C" and can be substantially more complex to interpret and communicate. Consider whether you have:

•Sufficient sample size to reliably estimate three-way interactions

•A clear theoretical rationale for why three-way interactions might exist

•A plan for interpreting and presenting them if significant

If any of these are not true, consider excluding three-way interactions from your model.