Two-Way ANOVA & Factorial Design

A set of Q&A flashcards covering definitions, calculations, and conceptual points about factorial designs and two-way ANOVA.

What distinguishes a factorial design from a single-factor design?

A factorial design includes two or more independent variables, whereas a single-factor design has only one independent variable.

How many independent variables are most common in factorial designs discussed in class?

Typically between 2 and 4, though in principle the number is unlimited.

What is a factorial matrix?

A table that displays every possible combination of all levels of all independent variables (i.e., all experimental conditions).

In a 2 × 2 factorial design, how many independent variables and levels per variable are there?

Two independent variables, each with two levels.

How many experimental conditions are produced by a 2 × 2 design?

Four conditions (2 × 2 = 4).

Why are the terms “levels” and “conditions” not interchangeable in factorial designs?

Levels refer to the categories within one independent variable, while conditions refer to the unique combinations of levels across all variables.

How many conditions are created in a 2 × 3 factorial design?

Six conditions (2 × 3 = 6).

Define a main effect in the context of a factorial design.

The overall effect of one independent variable, averaged across the levels of the other independent variable(s).

How is the number of possible main effects related to the number of independent variables?

They are equal; each independent variable contributes one main effect.

What is an interaction?

A situation in which the effect of one independent variable depends on the level of another independent variable.

Graphically, how can you tell there is NO interaction between two variables?

The plotted lines are parallel or have similar slopes.

When is a two-way ANOVA used?

When there are two independent variables, each with two or more levels, and you want to test main effects and their interaction.

Besides testing main effects and interaction, what follow-up can be performed after a significant two-way ANOVA?

Multiple-comparison (post-hoc) tests to pinpoint which specific condition means differ.

Name the four separate sources of variation calculated in a two-way ANOVA.

Variation due to rows (first IV), variation due to columns (second IV), variation due to interaction, and variation within conditions (error).

What is the F-ratio formula for the main effect of the rows variable?

Frows = (SSrows/dfrows) ÷ (SSwithin/df_within).

State the null hypothesis tested by each F-ratio in two-way ANOVA.

All relevant population means are equal (e.g., μ₁ = μ₂ = … = μₖ).

If an ANOVA null hypothesis is rejected, what conclusion can you draw?

At least one population mean differs, but ANOVA alone does not indicate which or by how much.

List the two primary assumptions of two-way ANOVA for independent groups.

(1) Populations are normally distributed; (2) Populations have equal variances (homogeneity of variance).

How sensitive is two-way ANOVA to violations of its assumptions when sample sizes are equal?

It is fairly robust; equal sample sizes reduce the impact of assumption violations.

What key advantage does a factorial design offer over conducting separate one-way ANOVAs?

It allows detection and interpretation of interactions between independent variables.