*Using alpha = .05, what is the F-critical? (three decimal places)*

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.

Learn how to calculate the F-critical value for an ANOVA with a significance level of alpha = 0.05. This problem involves understanding degrees of freedom, the F-distribution, and critical values. Suitable for advanced undergraduate students and researchers.

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