Overview of One-way ANOVA

• Focus on the study of the new serotonin-uptake inhibiting agent, SN-X95 in patients with General Anxiety Disorder (GAD).

Study Design

• Subjects: 52 subjects diagnosed with GAD.

• Groups: Randomly assigned to one of three treatment groups:

  • 25 mg SN-X95 (Lo-Dose)

  • 100 mg SN-X95 (Hi-Dose)

  • Placebo

• Duration: 10 weeks of daily oral dosing, double-blind study.

• Measurement Tool: Hamilton Rating Scale for Anxiety (HAM-A), scoring from 0 to 56 (higher indicates more anxiety).

Research Questions

• Random Variable: The HAM-A scores.

• Variable Type: Continuous variable.

• Parameter of Interest: Mean HAM-A test scores.

• Groups for Comparison: Three groups (Lo-Dose, Hi-Dose, Placebo).

Data Summary

• HAM-A scores (example data):

  • Lo-Dose (25 mg): 21, 18, 21, 26, various other scores.

  • Hi-Dose (100 mg): 16, 19, 22, various scores.

  • Placebo: 22, 18, 29, various scores.

• Dropouts: Patients without data are excluded from analysis.

• Summary Statistics of Groups:

  • Number of groups (k): 3

  • Total sample size (N): 48 (after excluding dropouts).

ANOVA Basics

• Purpose: Compare group means to analyze variability.

• Assumptions Required for One-way ANOVA:

  • Independent samples.

  • Normally distributed means.

  • Homogeneity of variances between groups.

Hypotheses

• Null Hypothesis (H0): No group effect; all group means are equal (µ1 = µ2 = … = µk).

• Alternative Hypothesis (H1): At least one group mean is different.

• F-Test Statistic: Approximated by F-distribution (F ~ F(k-1, n-k)).

• MSW: Mean Square Within-group, also referred to as Mean Square Error (MSE).

• MSB: Mean Square Between-group.

ANOVA Analysis Procedure

• One-way ANOVA Steps:

  • Calculate MSW and MSB.

  • Determine F-statistic.

• Goal: Analyze variability between and within groups to assess significant differences.

Results Interpretation

• If the p-value from ANOVA is less than significance level (typically 0.05), reject null hypothesis. Further multiple comparison tests are needed to identify specific group differences.

Multiple Comparisons

• Pairwise t-tests: Simple method for comparing group means but can inflate Type I error rate.

• Bonferroni Adjustment: Control overall error rate when performing multiple tests by adjusting significance level to α/c.

• Alternative Methods for Multiple Comparisons:

  • Tukey’s HSD: Less conservative, allows for all pairwise comparisons.

  • Dunnett’s Method: Specific comparisons against a control group.

  • Scheffe’s Method: More flexible but stringent in critical values.

Conclusion

• Lo-dose and high-dose groups showed significantly lower HAM-A scores compared to placebo, reinforcing the efficiency of SN-X95 in treating anxiety symptoms.