To find the F-critical value for an ANOVA, we need to know the significance level ($\alpha$), the degrees of freedom between groups ($df_{between}$), and the degrees of freedom within groups ($df_{within}$).

Given:

• $\alpha = 0.05$
• There are three groups (no treatment, psychotherapy, psychotherapy with medication), so $df_{between} = k - 1 = 3 - 1 = 2$
• The total number of participants $N = 15$, and there are 3 groups, so $df_{within} = N - k = 15 - 3 = 12$

Using these degrees of freedom, we can find the F-critical value from an F-distribution table or using statistical software.

Let me calculate the F-critical value for $\alpha = 0.05$, $df_{between} = 2$, and $df_{within} = 12$.

The F-critical value at $\alpha = 0.05$, $df_1 = 2$, and $df_2 = 12$ is approximately 3.885.

Would you like any further details or explanations?

Here are 5 questions you might ask next:

1. How do you calculate the F-ratio for this ANOVA?
2. What does the F-ratio represent in the context of ANOVA?
3. How do you interpret the results if the F-ratio exceeds the F-critical value?
4. Can you explain the steps involved in conducting an ANOVA test?
5. What is the purpose of post hoc tests after ANOVA?

Tip: Always check the degrees of freedom carefully when using statistical tables to ensure accurate critical values.