Two-Way ANOVA

Statistics · Axiom Academy

Understanding how to analyze the effects of two factors simultaneously on a response variable In two-way ANOVA, we examine two categorical factors (Factor A and Factor B) and how they affect a continuous response variable. This design allows us to study both factors at the same time rather than conducting separate one-way ANOVAs. Factor A: First categorical variable (e.g., teaching method with 3 levels) Factor B: Second categorical variable (e.g., student grade level with 2 levels) Cell: A unique combination of one level from Factor A and one from Factor B Replication: Multiple observations in each cell 2. Main Effects for Each Factor Two-way ANOVA tests three separate hypotheses: one for each factor's main effect, and one for the interaction between factors. H₀: All Factor A level means are equal (μ₁ = μ₂ = ... = μₐ) Hₐ: At least one Factor A level mean differs H₀: All Factor B level means are equal (μ₁ = μ₂ = ... = μᵦ) Hₐ: At least one Factor B level mean differs H₀: No interaction between Factor A and Factor B Hₐ: The factors interact (the effect of one factor depends on the level of the other) The two-way ANOVA table organizes all variance components and calculates test statistics for each hypothesis test. Source: Factor A, Factor B, Interaction (A × B), Error, Total SS: Sum of Squares for each source df: Degrees of freedom (a-1 for A, b-1 for B, (a-1)(b-1) for interaction, ab(n-1) for error) F: Test statistic = MS(effect)/MS(error)

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