F Critical Value Calculator

Find critical F-values for hypothesis testing (ANOVA, regression). Supports one‑tailed and two‑tailed tests with interactive F‑distribution visualization.

F‑distribution: Critical values define the boundary of the rejection region. For a given α and degrees of freedom, the critical F-value is the quantile that leaves α in the tail(s).

α=0.05, df1=1, df2=30
α=0.05, df1=3, df2=30
α=0.01, df1=2, df2=20
α=0.10, df1=5, df2=50
Two‑tailed, α=0.05, df1=3, df2=30
Computing...

Understanding F Critical Values

The F critical value is a threshold on the F‑distribution used in hypothesis testing (ANOVA, regression, variance ratio tests). It separates the rejection region from the non‑rejection region.

Definition: For a given significance level α and degrees of freedom (df1, df2), the critical value Fcrit satisfies:

  • Right‑tailed: P(F > Fcrit) = α
  • Left‑tailed: P(F < Fcrit) = α
  • Two‑tailed: P(F < Flower) = α/2 and P(F > Fupper) = α/2

If your observed F‑statistic falls in the rejection region (beyond the critical value), you reject the null hypothesis.

Common F Critical Values (α = 0.05, right‑tailed)

df1\df2 10 20 30 ∞
1 4.96 4.35 4.17 3.84
2 4.10 3.49 3.32 3.00
3 3.71 3.10 2.92 2.60
5 3.33 2.71 2.53 2.21

How to Use This Calculator

1

Set α and df: Choose your significance level (e.g., 0.05) and the numerator/denominator degrees of freedom from your study.

2

Select test type: Most F‑tests (ANOVA, regression) are right‑tailed. Use left‑tailed or two‑tailed for specific variance tests.

3

Optional observed F: Enter your calculated F‑statistic to see whether it exceeds the critical value and whether the result is significant.

Applications

  • ANOVA: Compare group means – reject if F > Fcrit.
  • Regression overall F‑test: Test model significance.
  • Equality of variances (F‑test): Often two‑tailed.
  • Lack‑of‑fit test: Assess model adequacy.

Calculator features:

  • Uses jStat library for precise F‑distribution quantiles
  • Interactive graph with shaded rejection region and critical lines
  • Optional observed F comparison with significance verdict
  • Adjustable decimal places for critical values
  • Displays both one‑tailed and two‑tailed critical values as needed

Frequently Asked Questions

A critical value is a point on the test distribution that is compared to the test statistic to decide whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you declare statistical significance.

In ANOVA and regression, the alternative hypothesis is that the model explains a significant amount of variance, which tends to produce large F‑values. Hence we reject only when F is sufficiently large (right tail).

The calculator uses jStat, which implements high‑accuracy numerical approximations. Results match standard F‑tables and statistical software (R, SAS, SPSS) to at least 4 decimal places.

For a two‑tailed F‑test (e.g., testing equality of variances), the calculator provides both lower and upper critical values. The rejection region consists of values below the lower critical or above the upper critical.

Yes, the calculator handles large df (e.g., 1000) accurately. As df increases, the F‑distribution approaches a normal distribution.