PY2501 Week 2 repeated measures ANOVA with one IV - Tagged

Page 1: Overview of the Lecture

• Title: Aston University Birmingham Lecture

• Topic: PY2501 Week 2

• Platform: vevox.app for participation

• Instructor: Ed Walford

• Lecture ID: 183-113-873

Page 2: Learning Outcomes

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

• Understand the purpose and function of one-way ANOVAs.

• Conduct one-way ANOVAs using the statistical software Jamovi.

• Interpret output results from Jamovi regarding one-way ANOVAs.

• Report results of one-way ANOVAs clearly and accurately.

Page 3: Introduction to One-Way ANOVA

• Definition: ANOVA (Analysis of Variance)

• Purpose: Identifies differences across three or more conditions.

• Parametric equivalent tests include:

  • Kruskal-Wallis test

  • Friedman test

• Context: These tests were covered in the previous year’s coursework.

Page 4: Types of One-Way ANOVA

• Two main types:

  • Within subjects/repeated measures ANOVA

  • Between subjects/independent groups ANOVA

• Characteristics:

  • Each type compares scores across 3 or more conditions.

  • Different menu commands and output formats in Jamovi.

Page 5: Function of ANOVA

• Objective: Analyze variance data.

• F statistic measures:

  • Ratio of between-condition variance (signal) vs. within-condition variance (error/noise).

• Formula: F = (Between condition variance) / (Within condition variance).

Page 6: Understanding the F Statistic

• Large F statistic indicates stronger differences between conditions as opposed to within conditions.

• Small F statistic suggests that variability within conditions dominates.

• Reporting: F < 1 implies more noise than signal, and thus is not significant.

Page 7: Comparison to T-Test

• Conceptually similar to t-test where:

  • F statistic balances group differences.

• Example: Comparing distances thrown by animals (cats, dogs, guinea pigs) by various team members.

• Design: Each athlete throws each type of animal, indicating repeated measures.

Page 8: Between and Within Group Differences

• Between-group differences refer to:

  • Signal variance observed among animals thrown.

• Within-group differences indicate:

  • Noise variance within repetitions of each animal type thrown.

Page 9: Variance Analysis with ANOVA

• ANOVA calculates:

  • Total variance between conditions (signal).

  • Total variance within conditions (noise).

• Ratio output informs us about the observed data distributions.

Page 10: Repeated Measures Example

• Hypothetical setup with 100 athletes throwing three animals (dog, cat, guinea pig).

• Data recorded in feet, negative scores possible if throws are erroneous.

• Data type: Interval level.

Page 11: Data Entry in Jamovi

• Structure: Three columns representing the distances thrown for each animal by each athlete.

Page 12: Normality Check

• Method: Use Exploration > Descriptives in Jamovi to validate normality.

• Important: Check Shapiro-Wilk statistics in the Descriptives dialogue under normality section.

Page 13: Interpreting Shapiro-Wilk Results

• Non-significant Shapiro-Wilk tests indicate the data can be treated as normally distributed for parametric analysis.

• If significant, consider Friedman’s non-parametric test or address outliers.

Page 14: Setting Repeated Measures in Jamovi

• Access ANOVA > Repeated Measures ANOVA.

• Input: Name the independent variable (IV) and all levels in ‘Repeated Measures Factors’.

• Assign variables into appropriate boxes for analysis.

Page 15: Requesting Additional Statistics

• Request:

  • Effect size eta2 (η2).

  • Sphericity tests (e.g., Mauchly’s test).

• These help validate the assumptions of the ANOVA.

Page 16: Output Interpretation

• Columns denote:

  • Sum of squares: raw variance amounts for between and within conditions.

  • Distinguishing residual variance between different athlete entries.

Page 17: Correction of Raw Variances

• Transform raw variances to Mean Square by dividing by degrees of freedom (df).

• Example calculations provided based on total observations and conditions.

Page 18: Calculating the F Ratio

• F ratio formulation: F = (MSanimal / MSwithin).

• Indicates the ratio between variance from the conditions vs. residual variance.

Page 19: ANOVA Results

• Example results: Non-significant (F (2, 198) = 2.84, p > .05).

• Interpretation: No need for post-hoc tests if overall differences are non-significant.

Page 20: Model Replication

• Scenario: Replication reveals similar means but less within-condition variance.

• Emphasis on reduced variability contributes to result significance.

Page 21: Significant Replication Results

• Example of significant result (F (2, 198) = 115, p < .001).

• Analysis of variance can substantially differ with varying within-condition dynamics.

Page 22: Understanding the F Statistic

• Core principle: The significance of the F statistic derives from the relationship between signal and noise.

Page 23: Effect Sizes in ANOVA

• Explanation of eta2 (η2) as a variance measure influenced by the independent variable conditions.

• Notation of significance alongside eta2, e.g., (F (2, 198) = 115, p < .001, η2 = .45).

Page 24: Evaluating η2 Effect Size

• Reference Cohen’s benchmarks for interpreting effect size:

  • Small: 0.01

  • Medium: 0.06

  • Large: 0.14

• Reporting effect sizes contextualizes findings effectively.

Page 25: Advantages of Eta Squared (η2)

• Interpretation of η2 as a proportion of explained variance.

• Comparison to Cohen’s d which measures standardized difference in conditions.

Page 26: Quick Quiz Announcement

• Platform: vevox.app

• Quiz ID: 183-113-873.

Page 27: Post Hoc Tests & Comparisons

• Discussion about the necessity of post hoc tests due to increased Type I error risk.

• Suggested corrections include Bonferroni corrections based on number of comparisons.

Page 28: Bonferroni Correction Explained

• Frequency of conduct: More comparisons lead to a heightened risk of Type I error.

• Demonstrating how to adjust the p-value threshold based on number of tests.

Page 29: Jamovi Handling of Corrections

• Note: Jamovi handles p-value corrections automatically during post hoc tests.

• Assurance to users that results remain significant as per standard values.

Page 30: Conducting Post Hoc Tests in Jamovi

• Navigate: Access Post Hoc Tests options; input independent variable.

• Various correction methods available with Tukey as the default.

Page 31: Output Results from Post Hoc Tests

• Importance of checking means and post-hoc outputs for significance.

• Specific comparison results provided for distance differences among animals.

Page 32: Obtaining Confidence Intervals

• Steps: Access ‘Estimated Marginal Means’ in Jamovi, input IV & enable tables for mean estimates & CIs.

Page 33: Final Output of Means & CIs

• Review of tables: mean distances and 95% CI ranges.

• Confidence interval overlaps validate prior analyses.

Page 34: Sphericity Tests

• Description: Sphericity tests assess variance equality in within-subject designs.

• Potential outcomes guide subsequent analysis adjustments.

Page 35: Interpreting Sphericity Results

• Mauchly’s test outcomes indicate whether adjustments are necessary.

• Correction choices depend on Epsilon values.

Page 36: Choosing Corrections for Sphericity

• Selection based on Greenhouse-Geiser: If > 0.75, use Huynh-Feldt correction; if < 0.75, use Greenhouse-Geiser correction.

Page 37: Impacts of Corrections on Outputs

• Corrections can affect Mean Square and df calculations, thus influencing result significance.

Page 38: Quick Quiz Recap

• Final quiz notice with instructions for participation via vevox.app.

Page 39: Looking Ahead

• Upcoming topic: Between subjects one-way ANOVA to be covered in the next lecture.

• Reminder for students to view recordings and post any queries.