1. What is the F Critical Value?

The F critical value is the threshold value from the F-distribution that determines whether the null hypothesis is rejected in an F-test. It depends on the significance level (α) and the degrees of freedom for the numerator (df₁) and denominator (df₂).

2. How Does the Calculator Work?

The calculator uses the inverse F-distribution function:

Where:

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

Explanation: The F critical value marks the boundary of the rejection region for the F-test. If the calculated F statistic exceeds this value, the null hypothesis is rejected.

3. Importance of F Critical Value

Details: The F critical value is essential for ANOVA tests, regression analysis, and comparing statistical models. It helps determine whether observed variances are statistically significant.

4. Using the Calculator

Tips: Enter the significance level (typically 0.05 or 0.01), and the degrees of freedom for both numerator and denominator. All values must be valid (0 < α < 1, df ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between F value and p-value?
A: The F value is the test statistic calculated from your data, while the p-value is the probability of obtaining that F value if the null hypothesis is true.

Q2: How do I choose the significance level?
A: Common choices are 0.05 (5%) or 0.01 (1%), depending on how strict you want to be about rejecting the null hypothesis.

Q3: What if my F statistic is exactly at the critical value?
A: By convention, we reject the null hypothesis when the test statistic is greater than the critical value.

Q4: Can I use this for one-way and two-way ANOVA?
A: Yes, but you need to use the correct degrees of freedom for each test.

Q5: Why does the F distribution have two degrees of freedom?
A: One for the between-group variability (numerator) and one for within-group variability (denominator).