This question appears to ask for a comparison of depression scores across three groups: Placebo, Low Dose, and Moderate Dose of an antidepressant. To analyze the data, an appropriate statistical test would depend on the design of the study and the distribution of the data.

Here’s how we can proceed:

Step 1: Identifying the Test

Since there are three groups being compared, and the data seem to represent continuous values (Beck Depression Inventory scores), the appropriate test would typically be a One-Way ANOVA (Analysis of Variance). This test checks whether there are statistically significant differences between the means of three or more independent groups.

Step 2: State the Hypotheses

• Null Hypothesis (H₀): There is no difference in the mean depression scores among the three groups (Placebo, Low Dose, Moderate Dose).
• Alternative Hypothesis (H₁): There is a significant difference in the mean depression scores among the groups.

Step 3: Data Preparation

The data is:

We would calculate the group means, group variances, and then conduct the ANOVA test.

Step 4: Post-ANOVA

If the ANOVA result is significant, we would follow it up with a post-hoc test (like Tukey's HSD) to determine which specific groups differ.

Would you like me to perform these calculations and provide the statistical output? Let me know if you'd prefer more details on each step.

Further Exploration Questions:

1. What are the assumptions of a One-Way ANOVA, and are they met here?
2. How would the results change if the groups had unequal sample sizes?
3. Can we test normality of the depression scores within each group?
4. What would the effect size (e.g., η²) tell us about the magnitude of the differences?
5. If ANOVA shows no significant difference, what could be alternative explanations?

Tip:

In statistics, always check assumptions like normality and homogeneity of variances before choosing a parametric test like ANOVA.