PY2501 Week 2 one way ANOVA - Tagged

Overview of One Way ANOVA

  • Course: Aston University Birmingham PY2501 Week 2

  • Instructor: Ed Walford

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 software Jamovi.

  • Interpret the output generated by Jamovi for one way ANOVAs.

  • Report the results of one way ANOVAs clearly and effectively.

What is ANOVA?

  • ANOVA stands for Analysis of Variance.

  • It analyzes the variance to determine if there are statistically significant differences between group means.

  • The result is an F statistic that provides a ratio of:

    • Between-condition variance (signal) vs Within-condition variance (noise).

    • The formula for F: F = Between condition variance / Within condition variance.

One Way ANOVA: Between-Subjects Design

Case Study Example

  • An employer wants to assess the performance of:

    • Recent Graduates

    • Individuals who attended a practical course

    • Individuals who completed a distance learning course.

  • They will compare test scores from these three groups to evaluate performance differences.

Design Elements

  • Independent Variable (IV): Education Group

    • Group Levels:

      • Graduates

      • Practical Course

      • Distance Learning

  • Dependent Variable (DV): Scores from the Jamovi test.

Data Entry in Jamovi

  • Similar to independent samples t-test but with multiple groups.

  • Use designations 1, 2, & 3 in the ‘group’ column and add labels in the ‘Levels’ box.

  • Input Jamovi test scores in a separate column under participants.

ANOVA Configuration in Jamovi

  1. Place IV in the ‘Grouping Variable’ box and DV in the ‘Dependent Variables’ box.

  2. Request descriptive tables and plots.

  3. Conduct Homogeneity and Normality tests under assumption checks.

  4. Choose between Welch’s or Fisher’s test based on homogeneity test results:

    • Welch’s for significant homogeneity test results.

    • Fisher’s for non-significant homogeneity test results.

Assumption Checks

  • Shapiro-Wilk Test: If significant, check for outliers and correct data or utilize the Kruskal-Wallis non-parametric test.

  • Levene’s Test: If significant, report this and opt for Welch’s test. If not significant, use Fisher’s.

Results Interpretation

  • A significant difference observed in test scores between the groups:

    • E.g., F(2, 57) = 36.01, p < .001.

  • Note: One way ANOVA does not directly provide effect sizes. Consider using separate ANOVA dialogues for effect sizes or calculate Cohen’s d for comparisons.

Post Hoc Tests

  • Necessary when differences exist but exact group comparisons are unclear.

  • If Levene’s test is non-significant, use Tukey’s post hoc tests.

  • If significant and Welch’s test is applied, use Games-Howell post hoc tests.

Reporting Results

  • Example: Graduate scores significantly different from Practical Course (t(57) = 6.54, p < .001) and Distance Learning (t(57) = 7.95, p < .001).

  • No significant difference between Practical and Distance Learning scores (t(57) = 1.41, p > .05).

Installing ESCI in Jamovi

  1. Click the ‘Analyses’ tab.

  2. Select the ‘Modules’ button.

  3. Browse and install the ‘esci’ module from the Jamovi library.

Descriptive Statistics Collection

  • Essential to compare average scores and interpret whether one group performed better or worse.

  • Use ESCI to generate means, standard deviations (SDs), and 95% Confidence Interval (CI) ranges.

Getting Detailed Descriptives

  1. Place variables in the appropriate Grouping and Dependent variable boxes within ESCI.

  2. Specify one group in ‘Combine into reference group’ and the others in ‘Combine into comparison group’ box.

  3. Access tables with descriptive statistics along with 95% CI ranges to understand group differences clearly.

Upcoming Topics

  • Introduction to Multiple ANOVA (with more than one IV).

  • Advantage of using the ANOVA dialogue in Jamovi for further options, including effect sizes.

  • Non-parametric alternative (Kruskal-Wallis) for scenarios lacking normality.

Reminders

  • Quiz and workshop participation is important.

  • Ensure proficiency in:

    • Understanding one way and repeated measures ANOVAs.

    • Conducting and interpreting results in Jamovi.

    • Clearly reporting statistical results.

Further Reading

  • Dancey & Reidy (2020). Statistics without Maths for Psychology. Chapter 10: Analysis of differences between 3 or more conditions (pp. 301-330).

  • Ignore SPSS content but compare output for ANOVA as Jamovi’s presentation is clearer.