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.