Interpreting Factorial ANOVA

Vocabulary flashcards covering key terms and concepts related to interpreting factorial ANOVA results, including main and interaction effects, F-statistics, critical values, and example applications.

Factorial ANOVA

An analysis of variance procedure that tests the effects of two or more independent variables (factors) simultaneously, including their interaction.

Between-subjects design

Experimental setup where each participant is exposed to only one condition or combination of factors.

Factor

An independent variable in ANOVA; in the lecture examples, factors include Dosage, Gender, Diet, and Training.

Level

A specific category or value of a factor (e.g., High vs. Low dosage, Male vs. Female gender).

2×2 Design

A factorial design with two factors, each having two levels (e.g., Dosage: High/Low × Gender: Male/Female).

Main Effect

The isolated impact of one factor on the dependent variable, averaged across the levels of the other factor(s).

Interaction Effect

Occurs when the effect of one factor on the dependent variable depends on the level of another factor.

Alpha Level (α)

The pre-set probability of Type I error; often .05 or .01, used as the cutoff for significance.

P-value

The probability of obtaining the observed F-value (or more extreme) if the null hypothesis is true; compared to α for significance.

Significance (ANOVA)

Conclusion that an effect exists when its p-value is less than α, leading to rejection of the null hypothesis.

F-Value

Ratio of a factor’s mean square to the error mean square (MSfactor / MSerror); used to test significance.

Critical F-Value

The cutoff value from the F-distribution table determined by α, numerator df, and denominator df; F-values above this are significant.

Degrees of Freedom (df)

Values describing the number of independent pieces of information; separate dfs exist for effects and error.

Numerator Degrees of Freedom

df associated with an effect (e.g., 1 for Gender, 2 for IV2 in practice problems) used in the F-ratio numerator.

Denominator Degrees of Freedom

Error df used in the denominator of the F-ratio (e.g., 24 or 44 in the examples).

Error Mean Square (MS_error)

Within-treatments variance estimate; the divisor in every F-ratio (also called Within MS).

Descriptive Statistics

Table of group means and standard deviations used to understand and interpret significant effects.

Effect Size

Quantitative measure of the magnitude of an effect; reported alongside p-values to assess practical importance.

Null Hypothesis (ANOVA)

Statement that there are no differences among group means or no interaction among factors.

Dosage Factor

Independent variable with High and Low levels in the drug effectiveness example.

Gender Factor

Independent variable with Male and Female levels in the drug effectiveness example.

Interpretation of Interaction

Determining how the relationship between one factor and the outcome changes across levels of another factor (e.g., high dose benefits males more than females).

Means Plot

Graph showing cell means; divergent or crossing lines suggest a potential interaction effect.

Rule of Thumb for Interaction

If the lines in a means plot intersect or are non-parallel, an interaction is likely present.

F-distribution Table

Reference table that lists critical F-values for combinations of numerator and denominator dfs at chosen α levels.

Within-Treatments Variance

Variation of scores inside each group; basis for MS_error.

Between-Treatments Variance

Variation among group means attributed to experimental manipulations; source for MS_effect.

Research Question

Guiding inquiry that the ANOVA seeks to answer (e.g., Does drug effectiveness differ by dosage and gender?).

Practice Problem #1

Worked example showing calculation of F-values (15, 16.25, 1.25) and identification of significant main effects only.

Practice Problem #2

Contextual example (diet × training) demonstrating significance at α = .01 for main effect of training and the interaction.