module 3 stat part 6

Introduction to ANOVA

• ANOVA (Analysis of Variance) is used to compare means across multiple groups.

• The F statistic from ANOVA informs if at least one group mean differs from the others.

Understanding Group Differences

• Example: Analyzing anxiety scores across three therapy groups (A, B, C).

  • Group A: 5 hours therapy.

  • Group B: 10 hours therapy.

  • Group C: 15 hours therapy.

• Possible scenarios for group means:

  • All means are different.

  • Some means are equal, but others differ.

Post Hoc Testing

• When the null hypothesis is rejected (i.e., at least one mean differs), post hoc tests identify which means are different.

  • Preferable to multiple t-tests to control type 1 error rates.

  • Example tests include Tukey's test.

ANOVA Results Interpretation

• Jamovi results for anxiety scores revealed:

  • Comparison A vs B: Mean difference = -10.62, p < 0.001 (significant difference).

  • Comparison A vs C: Mean difference = -1.79, p = 0.665 (not significant).

  • Comparison B vs C: Mean difference = 8.83, p < 0.001 (significant difference).

• Visual representation can enhance understanding; significance can be indicated with asterisks ( ***).

Reporting Results

• Example of reporting results:

  • "Mean anxiety score for group B significantly different from A and C (p < 0.001)."

Analysis of Variance Steps

1. Assumptions check: Normal distribution, equal variances, independence.

2. Conduct ANOVA with null hypothesis that all means are the same.

   • If p > 0.05, accept the null hypothesis.

   • If p < 0.05, reject the null hypothesis and proceed to post hoc testing.

Assumptions Verification

• Normality and Equal Variances:

  • Utilize Levene's test for variance equality.

  • If variances are unequal, consider Welch's F-test for adjustments.

• If assumptions are violated: Use nonparametric alternatives (e.g., Kruskal-Wallis test).

Further Example: HV Study on Height

• Groups: Asia Pacific, European, Other.

• Check for independence - confirmed as different individuals.

• Normality assessed with box plots and mean-median comparisons.

• Variance equality confirmed with Levene’s test (p = 0.86).

• Conduct ANOVA with F-statistic = 3.49, p = 0.036, indicating at least one mean is different.

• Post hoc results showed:

  • Significant difference between Asia Pacific and European group (mean difference = -6.8, p = 0.035).

  • No strong evidence for differences with other comparisons.

Consistency in Results Reporting

• Results should match earlier bivariate analyses; box plots can provide visual reinforcement.

• Example summary of analysis:

  • "At least one ethnic group's mean height is different, with specific significant differences noted in comparisons."

Recap of ANOVA process:

• ANOVA compares more than two group means, determining between-group and within-group variations.

• Used to guide decisions based on statistical significance and comparisons.