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Mixed ANOVA

Mixed Factorial Design & Analysis (Mixed ANOVA)

  • Instructor: Dr. Victoria Wright

  • Course: PS21310 2024-25

Today’s Session

  • Objectives:

    • Run the 2x2 mixed factorial ANOVA

    • Report the main effects

    • Report and interpret the interaction effect

What Does an ANOVA Actually Do?

  • ANOVA produces a statistic known as F.

  • F is defined as the ratio of systematic variation to unsystematic variation.

  • If the null hypothesis is true, the F value will approach 1.

  • A large F value suggests a greater systematic variation compared to unsystematic variation.

Factorial ANOVA

  • One-way ANOVA: involves the manipulation of one independent variable (IV).

  • Factorial ANOVA: involves the manipulation of two or more IVs.

    • Two-way ANOVA: manipulates 2 IVs.

    • Three-way ANOVA: manipulates 3 IVs.

    • Four-way ANOVA: manipulates 4 IVs.

Factorial ANOVA: Types

  • Fully Between Subjects: All IVs are tested between subjects/independent measures.

  • Fully Within Subjects: All IVs are tested within subjects/repeated measures.

  • Mixed Factorial: One or more IVs are between subjects, and one or more IVs are within subjects.

2x2 Mixed Factorial ANOVA: Assumptions

  • Data must be on an interval or ratio scale.

  • Assumptions include:

    • Normality

    • Homogeneity of variance

    • Sphericity (applies if an IV has 3 or more levels).

  • Example: Levene’s test indicates homogeneity of variance was met, F(3,28) = 1.053, p = .410.

2-Way Mixed ANOVA: Results

  • Considerations include:

    • Main Effect 1 (Between Subjects)

    • Main Effect 2 (Within Subjects)

    • Interaction effects.

2x2 Mixed Factorial ANOVA: Example

  • Factor 1 (Between Subjects): Language Group (Monolingual or Bilingual)

  • Factor 2 (Within Subjects): Response inhibition trial type (Go and No Go)

  • Dependent Variable (DV): Response Accuracy (%)

  • Prediction: Bilinguals will have stronger inhibitory control with fewer errors on No Go trials.

  • Main Effect 1: Language Status.

  • Main Effect 2: Trial Type.

  • Interaction: Higher response accuracy for bilinguals on No Go trials.

2x2 Mixed Factorial ANOVA: SPSS

  1. Analyze > General Linear Model > Repeated Measures.

  2. Enter repeated/WS factor name in "Within Subjects Name" box, enter the number of levels (2) and add it.

  3. Click "Define" after setup.

Setting Up in SPSS

  • Assign Go trials and No Go trials to the Within Subjects Variables box.

  • Order: Go = 1, No Go = 2.

  • Assign Language Status to the Between Subjects factor box.

SPSS Options

  • Request Plots as performed previously.

  • In Options, request Descriptives and Homogeneity Tests.

  • For EMMeans, transfer all items to the right, select Compare Main Effects and Simple Main Effects, and choose Bonferroni from the drop-down menu.

Reporting the Main Effects in SPSS

  • Analyze to get Descriptives (means and SDs).

  • Check Levene’s test of homogeneity.

  • Evaluate:

    1. Is the interaction significant?

    2. Are the main effects significant?

2-Way Mixed ANOVA: Results

  • Main Effect 1 (BS)

  • Main Effect 2 (WS)

  • Interaction:

    • Assess influence of language group on accuracy.

    • Assess influence of trial type on accuracy.

    • Evaluate if bilinguals are better at inhibiting a response (No Go).

Between-Subjects Effect (Independent Measures)

  • Check significance of the between-subjects factor (Language Status).

  • Refer to the Test of Between-Subjects Effects for performance comparison.

Within-Subjects Effect (Repeated Measures)

  • Check significance of the within-subjects factor (Trial Type).

  • Refer to the Test of Within-Subjects Effects for performance comparison.

2-Way Mixed ANOVA: Interaction Effect

  • Assess the significance of the interaction between Trial Type and Language Status.

  • Analyze the Test of Within-Subjects Effects for details.

Interaction Effect Analysis

  • Plots suggest both groups were equally accurate in Go trials.

  • Bilinguals showed higher accuracy than Monolinguals in No Go trials; check for significance.

Pairwise Comparison Results

  • No significant difference in Go trials between Monolinguals (M = 89.6) and Bilinguals (M = 88.30), p = .644.

  • Significant difference for No Go trials; Bilinguals (M = 92.4) were much more accurate than Monolinguals (M = 73.90), p < .001.

Reporting the Main Effects

  • Significant main effect of Language Status:

    • F(1,18) = 15.731, MSE = 739.600, p < .05.

    • Bilinguals (M = 90.35%) were significantly more accurate than Monolinguals (81.75%).

Reporting the Trial Type Effect

  • Significant main effect Trial Type:

    • F(1,18) = 7.162, MSE = 336.400, p > .05.

    • Responses were more accurate in Go trials (88.95%) compared to No Go trials (83.15%).

Reporting the Interaction Effect

  • Significant interaction of language status and trial type:

    • F(1,19) = 20.87, MSE = 980.100, p < 0.001.

    • Followed by Bonferroni-corrected t-tests, results indicate:

      • No significant difference in accuracy for Go trials between Mono (89.6%) and Bilinguals (88.3%), p = .644.

      • Bilinguals were significantly more accurate than Monolinguals for No Go trials.

Conclusion of Today’s Session

  • Competency gained:

    • Running the 2x2 mixed factorial ANOVA

    • Reporting main effects

    • Interpreting interaction effects.