Module 5: Factorial ANOVA (independent designs)

Comprehensive vocabulary flashcards covering factorial ANOVA experimental designs, variance partitioning, assumptions, main effects, interaction effects, simple effects, and effect sizes.

Factorial ANOVA

A statistical test used to evaluate differences in group means when a research design includes more than one independent variable (factor), allowing researchers to test both main effects and interactions.

Factor

An alternative, interchangeable term for an independent variable ($\text{IV}$) in an ANOVA design, which contains two or more levels.

Main Effect

The direct effect of a single independent variable on a dependent variable, testing whether mean scores differ across its levels while collapsing across or ignoring the levels of any other independent variables.

Interaction Effect

An effect that occurs when the impact or difference of one independent variable on the dependent variable depends upon the specific level of another independent variable.

Simple Effects

The effect of an independent variable at a single, specific level of another independent variable, typically evaluated using pairwise comparisons between cell means following a significant interaction.

Cell Means

The mean scores of the dependent variable for each individual experimental condition or unique combination of levels across all independent variables.

Marginal Means

The mean scores across each individual level of an independent variable, calculated by averaging across (and ignoring) the levels of the other independent variable(s).

Two-Way Independent ANOVA

A factorial ANOVA design evaluating two between-subjects independent variables, where each participant is assigned to only one experimental condition.

Primary IV (PSYC21061 rule)

A specific course rule designating the first independent variable introduced or referred to in the research question or design statement.

Secondary IV (PSYC21061 rule)

A specific course rule designating the second independent variable mentioned, upon which the effect of the primary independent variable may depend.

Two-Way Repeated Measures ANOVA

A factorial ANOVA design where all independent variables are within-subjects, meaning every participant is measured under every condition.

Two-Way Mixed ANOVA

A factorial ANOVA design that combines at least one between-subjects independent variable and at least one within-subjects independent variable.

$2 \times 2$ Factorial Design

An experimental design with two independent variables (factors), each having exactly two levels, yielding a total of four conditions.

$2 \times 4$ Factorial Design

An experimental design containing two independent variables, where one factor has two levels and the second factor has four levels, resulting in eight conditions.

$4 \times 2 \times 2$ Factorial Design

A factorial design with three independent variables, where the first factor has four levels and the remaining two factors have two levels each.

Homogeneity of Variance

The parametric ANOVA assumption stating that the population variance of the dependent variable must be approximately equal across all experimental conditions.

Levene's Test

An inferential statistical test used to test the null hypothesis that the error variances of the dependent variable are equal across all groups or conditions.

Normality Assumption (Factorial ANOVA)

The requirement that the dependent variable is approximately normally distributed in the population within each individual experimental condition.

Independence of Observations

The assumption that each participant contributes exactly one score that is completely independent of the scores of any other participant in the study.

Classical Eta Squared ($\eta^2$)

An effect size measure representing the proportion of the total variance in the dependent variable that is attributable to a specific experimental effect: $\eta^2 = \frac{SS_M}{SS_T}$.

Partial Eta Squared ($\text{Partial } \eta^2$)

An effect size measure representing the proportion of variance associated with an effect after excluding the variance explained by other effects: $\text{Partial } \eta^2 = \frac{SS_M}{SS_M + SS_R}$.

Residual Variance ($SS_R$ / Error Variance)

The within-condition variance in an ANOVA model that remains unexplained by the experimental factors, reflecting individual differences and experimental error.

Model Sum of Squares ($SS_M$)

The amount of total variation in the dependent variable explained by a specific experimental effect, such as a main effect or an interaction.

Post Hoc Tests (Factorial ANOVA)

Pairwise comparisons conducted between marginal means only when a factor's main effect is statistically significant and that factor has more than two levels.

Tukey HSD

A standard post hoc test used to perform pairwise comparisons between marginal means while maintaining the overall familywise error rate at $\alpha = .05$.

Bonferroni Correction

A multiple comparison correction procedure that reduces the risk of Type I errors by dividing the required alpha level ($\alpha$) by the total number of comparisons ($c$): $\alpha_{\text{adjusted}} = \frac{\alpha}{c}$.

Cohen's $d$ (in Simple Effects)

The standardized effect size index calculated and reported alongside follow-up pairwise $t$-tests when evaluating simple effects.

Profile Plot

A visual plot of estimated marginal means or condition means displaying separate lines for levels of one factor across levels of another to inspect interaction patterns.

Null Hypothesis for a Main Effect ($H_0$)

The hypothesis stating that population marginal means are equal across all levels of a given independent variable, collapsing across any other variables.

Null Hypothesis for an Interaction ($H_0$)

The hypothesis stating that the differences between the levels of one independent variable are identical across all levels of the other independent variable in the population.

$F$-ratio for an Interaction

The test statistic computed by dividing the mean square of the interaction by the mean square residual (error): $F = \frac{MS_{\text{interaction}}}{MS_R}$.

Mean Square ($MS$)

An estimate of population variance obtained by dividing a sum of squares ($SS$) by its associated degrees of freedom ($df$): $MS = \frac{SS}{df}$.

Corrected Model (SPSS)

The row in an SPSS ANOVA table representing the combined variance accounted for by all main effects and interaction terms combined.

Type I Error Rate Inflation

The escalation of the cumulative probability of finding at least one false positive result when conducting multiple statistical hypothesis tests without alpha correction.

Three-Way Independent ANOVA

A factorial design involving three between-subjects independent variables, partitioning variance into three main effects, three two-way interactions, one three-way interaction, and error.