1. What is the F Critical Value?

The F critical value is the threshold value from the F-distribution that separates the rejection region from the non-rejection region in hypothesis testing. It's used in ANOVA and regression analysis to determine statistical significance.

2. How Does the Calculator Work?

The calculator uses the inverse F-distribution:

Where:

• \( \alpha \) — Significance level (probability threshold)
• \( df_1 \) — Numerator degrees of freedom
• \( df_2 \) — Denominator degrees of freedom

Explanation: The calculator finds the value on the F-distribution where the cumulative probability equals 1-α for given degrees of freedom.

3. Importance of F Critical Value

Details: The F critical value is essential for determining whether to reject the null hypothesis in F-tests, including ANOVA and comparing nested regression models.

4. Using the Calculator

Tips: Enter a significance level between 0 and 1 (typically 0.05), and positive integer values for both degrees of freedom.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between F value and F critical value?
A: If calculated F > F critical, reject the null hypothesis; otherwise, fail to reject it.

Q2: How do degrees of freedom affect the critical value?
A: As df increase, the F distribution becomes more concentrated and critical values decrease.

Q3: What's a typical significance level?
A: α = 0.05 is common, but 0.01 or 0.10 may be used depending on the field.

Q4: Can I use this for one-tailed tests?
A: Yes, the calculator provides the critical value for one-tailed F-tests.

Q5: What if my test statistic equals the critical value?
A: This is exactly at the threshold. Convention is to not reject the null in this case.