Understanding Interactions in Two-Way ANOVA: Behavioral Sciences, Study notes of Statistics for Psychologists

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Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

Ch. 15. Two-way ANOVA (Independent Measures) I. Situation and terminology A. Situation: Two factors (IV) to manipulate or classify. B. Terminology

1. Factor: A manipulation or classification scheme (cf. independent variable).
2. Level: Number of groups within each factor.
3. Cell: A group formed by combination of the levels of the factors (e.g., 2x3, 4x5, 3x4x6).
4. In a two-way ANOVA, we have three hypotheses, two for two main effects and one for one interaction effect.
5. Main effect: A constant effect due to one factor, main effect A and main effect B.
6. Interaction effect: The unique effect of combinations of two main effects; the effect of one factor depends on the level of the second factor (pp. 470-473).

C. Procedure

1. For main effect A: H 0 : μ 1 = μ 2 = ⋅ ⋅ = μa. H 1 : H 0 is not true. For main effect B: H 0 : μ 1 = μ 2 = ⋅ ⋅ = μb. H 1 : H 0 is not true. For interaction effect. H 0 : No interaction effect. H 1 : H 0 is not true.
2. α: .05 or .01 for all three hypotheses. Fcrit for each hypothesis based on df's.
3. TS: FA = MSA/MSE, MSA = SSA/dfA = SSA/a- FB = MSB/MSE, MSB = SSB/dfB = SSB/b- FAB = MSAB/MSE, MSAB = SSAB/dfAB = SSAB/(a-1)(b-1) MSE =SSE/dfE = SSE/ab(n-1)
4. Decision: If Fobs≥Fcrit, reject H 0.

D. Two-way ANOVA Summary Table Source df SS MS F A a-1 SSA SSA/dfA MSA/MSE B b-1 SSB SSB/dfB MSB/MSE A*B (a-1)(b-1) SSAB SSAB/dfAB MSAB/MSE Error ab(n-1) SSE SSE/dfE ────────────────────────────────────────────── Total nab-1 SST E. Assumption; same as one-way ANOVA. F. Example G. Advantages over two one-way ANOVAs.

1. The savings of subjects.