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N-Way within and mixed ANOVA - Tagged

Aston University Birmingham 2+ way Within and mixed designs ANOVAs

  • Presenter: Ed Walford

Learning Outcomes

  • By the end of the week’s activities, you should be able to:

    • Understand mixed and within-subjects multiple ANOVAs.

    • Analyze mixed and within-subjects multiple ANOVAs in Jamovi.

    • Interpret mixed and within-subjects multiple ANOVA outputs in Jamovi.

    • Report results from mixed and within-subjects multiple ANOVAs.

Mixed and Within Subjects Multiple ANOVAs

  • Definition of Mixed ANOVA:

    • Involves at least one between-subjects IV/factor and at least one within-subjects IV/factor.

  • Definition of Within Subjects Multiple ANOVA:

    • Involves at least two within-subjects factors.

  • Similar functionality to between-subjects ANOVAs discussed previously.

Example: Mixed Two Way ANOVA

  • Research Scenario: A developmental psychologist studies the pretend play time of children during school breaks.

    • Investigates differences by gender (boys vs. girls) and across different times of the year (winter, spring, summer).

    • Data collected from two reception classes over one month.

    • Total hours spent in pretend play recorded for 20 boys and 20 girls.

Identifying IVs and DVs

  • Independent Variables (IVs):

    • Between Subjects IV: Gender (2 levels: male, female).

    • Within Subjects IV: Term (3 levels: winter, spring, summer).

  • Dependent Variable (DV):

    • Total hours spent in pretend play.

Terminology

  • IV: Also referred to as factors.

  • Conditions/Groups: Referred to as levels of an IV/factor.

Jamovi Data Entry

  • Set up:

    • One column for gender (1 = male, 2 = female).

    • Separate columns for mean hours of pretend play during winter, spring, and summer terms.

  • Measure Type:

    • Gender as nominal, hours of pretend play as continuous.

Within Subjects Conditions

  • Ensure all levels for within subjects conditions (winter, spring, summer) have been defined as continuous.

Conducting ANOVA in Jamovi

  • Access through: ANOVA > Repeated Measures ANOVA.

    • Fill in names of levels for within-subjects factors.

    • Drag the appropriate variables into the displayed boxes.

    • Input the dependent variable and assign a name to the within-subjects factor.

    • Ask for 2 (eta2) effect size.

Output Interpretation

  • Interaction between gender and season: Significant with large effect size (29% variance explained).

  • Main effect of gender: Significant with very large effect size (57% variance explained).

  • Main effect of season: Not significant (0.2% variance explained).

Post-Hoc Analysis

  • Important to conduct descriptives, post hoc tests, and 95% CI ranges for interpretation.

    • Post hoc tests are not needed for the non-significant main effect of season.

    • They can help interpret significant interactions.

Interaction Analysis

  • Significant gender differences in spring and summer, absent in winter.

  • No gender differences in winter (p = .42), indicating season impacts gender's influence on play.

Estimated Marginal Means Dialogue

  • Input IVs into appropriate slots in the dialogue box.

  • Request marginal means plots and tables.

Season Main Effect

  • No overall differences in hours of pretend play across all seasons.

    • Means overlap and are consistent with non-significant findings.

Gender Main Effect

  • Significant results indicate males engage in significantly more pretend play than females, supported by overlapping confidence intervals.

Interaction Analysis

  • Confirms gender differences do not exist in winter; differences appear in spring and summer.

  • Confidence intervals for spring and summer do not overlap, indicating significant differences.

Quick Quiz

  • Recap of learned concepts.

Finalizing Tables

  • Complete tables with standard deviation (SD) values, removing standard errors (SE).

    • Use Exploration > Descriptives to request standard deviations for interactions and report them in the tables.

Reporting ANOVA Results

  • Break down into separate analyses:

    • Report two main effects (gender, term) and their interaction.

    • Start with descriptives for each analysis and move to inferential statistics.

Term Main Effect Results

  • Not significant (F (2, 76) = 1.11), indicating little variation in means across terms.

Reporting Gender Main Effect

  • Detailed reporting on mean hours of pretend play for each gender, indicating substantial differences in playtime (F (1, 38) = 321.96, p< .001).

Reporting Interaction Results

  • Interaction is significant, and presented results clarify specific conditions leading to observed differences.

Multiple Within Subjects ANOVA

  • Scenario: A psychologist studies offensive language use by following 20 fans across six matches, analyzing the effect of match location and result.

Data Setup for ANOVA

  • Within subjects 3 (result: win, lose, draw) x 2 (venue: home, away) ANOVA.

  • Requires setup of six continuous variables in Jamovi.

Data Entry for ANOVA

  • Ensure all variable names are appropriate and defined as continuous.

Conducting Analysis in Jamovi

  • Follow similar steps to previous ANOVA, defining factors and level variables appropriately.

Results Interpretation

  • Significant findings for venue and result; provide effect sizes and clarity on interaction.

Assumption Checks

  • Ensure sphericity tests are checked; apply corrections as necessary based on outcomes.

Post-Hoc Testing

  • Required only for IVs with three levels or more; conduct for Result IV and interactions.

Final Reporting

  • Report mean differences and significant post hoc findings.

  • State clear observations with supporting effect sizes.

Conclusion

  • Understand and analyze mixed and within-subjects multiple ANOVAs using Jamovi.

  • Complete workshop tasks, quizzes, and reading assignments.

Reading and Additional Resources

  • Reference: Dancey & Reidy (2020) "Statistics Without Maths for Psychology" (pp. 331-378); focus on mixed and within-subjects ANOVA.