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.