What Is an F Table?
An F table lists critical values for right-tailed F-tests used in ANOVA, regression, and variance testing. Select your significance level (α), find numerator degrees of freedom (df1) in the columns and denominator degrees of freedom (df2) in the rows. The value at their intersection is the F critical value. If your calculated F-statistic equals or exceeds this value, the result is statistically significant and you reject the null hypothesis.
F Critical Value Calculator
Click any cell to highlight the critical value. All values are right-tail critical values Fα,(df1,df2). Columns = numerator df1, Rows = denominator df2.
What Is the F Distribution?
Definition
The F distribution is a ratio of two chi-squared distributions, each divided by its degrees of freedom. It is right-skewed, always positive, and defined by two parameters: numerator df (df1) and denominator df (df2). It is written as F(df1, df2).
Key Properties
F values are always ≥ 0. The distribution is right-skewed — not symmetric — so critical values are read from the right tail only. As df1 and df2 both grow large, the F distribution approaches normality.
Named After
The F distribution is named after Sir Ronald Fisher, who developed it in the 1920s. George W. Snedecor later tabulated it, which is why you sometimes see it called Snedecor's F distribution or the variance ratio distribution.
When to Use the F Table
The F table applies to four main test types. Each uses the same lookup process but computes degrees of freedom differently.
One-Way ANOVA
Comparing three or more group means. df1 = k − 1 (k = groups), df2 = N − k (N = total observations). The most common F-table use case.
Regression F-Test
Testing overall significance of a regression model. df1 = number of predictors (p), df2 = n − p − 1. A significant result means at least one predictor explains variance.
Equality of Variances
Testing whether two populations have equal variances. df1 = n1 − 1, df2 = n2 − 1. For two-tailed tests, use α/2 to find each critical value.
Two-Way ANOVA
Testing two factors and their interaction simultaneously. Each effect — Factor A, Factor B, and A×B interaction — has its own df1, df2, and separate F critical value.
How to Read the F Table: Step-by-Step
Reading an F table is a four-step process. Once you know your significance level and both degrees of freedom, the table gives you the exact threshold for your decision.
How to Find the P-Value from an F Table
The F table gives critical values, not exact p-values. However, you can bracket the p-value by comparing your F-statistic against the α = 0.10, 0.05, 0.025, and 0.01 columns for your df combination.
Example: Your ANOVA gives F = 4.10 with df1 = 2, df2 = 30. Look up F(2, 30) in each α table:
| Significance Level (α) | F critical value F(2,30) | Your F = 4.10 vs critical |
|---|---|---|
| α = 0.10 | 2.489 | 4.10 > 2.489 ✓ |
| α = 0.05 | 3.316 | 4.10 > 3.316 ✓ |
| α = 0.025 | 4.182 | 4.10 < 4.182 ✗ |
| α = 0.01 | 5.390 | 4.10 < 5.390 ✗ |
For the exact p-value, use statistical software:
Excel
=F.DIST.RT(4.10, 2, 30)
// Returns: 0.0271
R
pf(4.10, 2, 30, lower.tail=FALSE)
# Output: 0.02709
Python
from scipy import stats
stats.f.sf(4.10, 2, 30)
# Output: 0.02709
How to Use the F Table for a Two-Tailed Test
The standard F table is built for right-tailed tests. For a two-tailed variance equality test (H₀: σ₁² = σ₂²), you need both an upper and a lower critical value.
Degrees of Freedom Calculator for F-Tests
Select your test type, enter the required values, and get df1 and df2 instantly.
Worked Examples: Using the F Table
Three examples cover the most common F-table scenarios: comparing group means, testing a regression model, and checking variance equality.
Example 1One-Way ANOVA — Three Teaching Methods
Scenario: A researcher compares exam scores across three teaching methods, with 10 students per group (N = 30) at α = 0.05.
Example 2Multiple Regression F-Test — Predicting Sales
Scenario: A regression model has 4 predictors and 50 observations. Test overall model significance at α = 0.05.
Example 3Equality of Variance F-Test (Two-Tailed)
Scenario: Test whether two production lines have equal variance. Line 1: n1 = 21, Line 2: n2 = 16. Use α = 0.05 (two-tailed, so use α/2 = 0.025 per tail).
F Table vs t-Table vs Chi-Square Table
Each table covers a different family of tests. The key distinction comes down to what you are comparing and how many groups are involved.
| Feature | F Table | t-Table | Chi-Square Table |
|---|---|---|---|
| Distribution shape | Right-skewed | Symmetric | Right-skewed |
| Parameters | df1 and df2 | df only | df only |
| Primary use | ANOVA, regression | Mean comparison (1–2 groups) | Categorical data, goodness-of-fit |
| Always positive? | Yes (≥ 0) | No (both tails) | Yes (≥ 0) |
| Relationship | F(1,df) = t² | t² = F when df1=1 | F = χ²/df (ratio form) |
Finding F Critical Values Without a Table
Statistical software gives exact F critical values for any df combination, especially useful when your df falls between printed table values.
Excel
=F.INV.RT(0.05, 3, 27)
// Returns: 2.9604
=F.INV.RT(alpha, df1, df2)
Older Excel: use FINV(alpha, df1, df2)
R
qf(p = 0.95, df1 = 3, df2 = 27)
# Output: 2.960351
# Note: use 1−α for right tail
Use 1 − alpha as the probability argument
Python
from scipy import stats
stats.f.ppf(q=0.95,
dfn=3, dfd=27)
# Output: 2.960351
scipy.stats.f.ppf gives the quantile function
Assumptions of the F-Test
Valid F-test results require three conditions. The F-test is reasonably robust to mild violations of normality with large samples, but violations of independence are more serious.
1. Independence
Observations within and between groups must be independent. Violating this assumption — such as repeated measures without correction — invalidates the standard F-test.
2. Normality
Each group's data should be approximately normal. The F-test is robust to mild non-normality when sample sizes are large, but check with a Q-Q plot or Shapiro-Wilk test for small samples.
3. Homogeneity of Variance
Group variances should be approximately equal (homoscedasticity). Test with Levene's test or Bartlett's test before running ANOVA. If violated, use Welch's ANOVA instead.
Common Mistakes When Using the F Table
F Table PDF — Free Download
Download printable F distribution tables in PDF format. Each version includes critical values for standard significance levels and covers a full range of degrees of freedom.
F Table: Most Commonly Referenced Critical Values
These F critical values appear most often in textbooks, homework problems, and published research.
F Distribution: Key Facts
Frequently Asked Questions About the F Table
What is an F table?
An F table (F distribution table) is a statistical reference listing critical F values for right-tailed hypothesis tests. To use it, select the correct significance level (α), find numerator df1 in the columns and denominator df2 in the rows, and read the critical value at their intersection.
How do you read the F table?
Select the table for your significance level (α). Columns represent numerator df (df1) and rows represent denominator df (df2). The cell at the intersection of your df1 column and df2 row is the critical F value. Reject H₀ if F-calculated ≥ this value.
How do you read the F table for ANOVA?
For one-way ANOVA, compute df1 = k − 1 (number of groups minus 1) and df2 = N − k (total observations minus number of groups). Select the α = 0.05 tab. Find your df1 column and df2 row. The intersection value is F-critical. If your computed F-statistic is greater than or equal to F-critical, at least one group mean differs significantly from the others.
What is the F critical value at df1=3, df2=30, α=0.05?
F(3, 30) at α = 0.05 has a critical value of 2.92. Any calculated F-statistic equal to or greater than 2.92 is statistically significant at the 5% level. Use the calculator at the top of this page to look up any combination of df1, df2, and α.
How do you find the p-value from an F table?
The F table doesn't give exact p-values, but you can bracket them. Compare your F-statistic against the α = 0.10, 0.05, 0.025, and 0.01 critical values for your df. If F falls between the 0.05 and 0.025 thresholds, then 0.025 < p < 0.05. For an exact p-value use Excel: =F.DIST.RT(f, df1, df2), R: pf(f, df1, df2, lower.tail=FALSE), or Python: scipy.stats.f.sf(f, df1, df2).
How do you use the F table for a two-tailed test?
For a two-tailed F-test at α = 0.05, use α/2 = 0.025 per tail. Use the α = 0.025 tab to find the upper critical value Fupper(df1, df2). The lower critical value is Flower = 1 ÷ F(df2, df1) — the reciprocal with the degrees of freedom swapped. Reject H₀ if your F-statistic ≥ Fupper or ≤ Flower.
What is the difference between α = 0.05 and α = 0.01 in the F table?
The α = 0.01 table has higher critical values, requiring a larger F-statistic to reject H₀. For example, F(2, 30) at α = 0.05 is 3.32, but at α = 0.01 it rises to 5.39. Stricter tests reduce Type I error (false positives) but make it harder to detect real effects.
What does a significant F-test mean?
A significant F-test means the between-group variance is large relative to within-group variance — indicating at least one group mean or predictor has a statistically significant effect. In ANOVA, follow up with post-hoc tests to identify which groups differ.
What if my degrees of freedom are not in the F table?
Round down to the next lower listed df value — this gives a slightly more conservative (higher) critical value, which controls Type I error. For df2 greater than 120, use the ∞ row. For exact values, use Excel's F.INV.RT(), R's qf(), or Python's scipy.stats.f.ppf(). This page's calculator also handles any df combination.
Is F = t² always true?
Only when df1 = 1. F(1, df) equals t²(df), so both tests give the same p-value in that case. For ANOVA comparing three or more groups, the F-test has no equivalent in the t-distribution.
Related Statistical Tables & Resources
Understanding the F Table: What the Values Mean
What the α Level Means
Each table corresponds to one α value: the probability of rejecting H₀ when it is actually true (Type I error). α = 0.05 gives a 5% false positive rate. Smaller α reduces false positives but demands a larger F-statistic to reach significance.
Why Larger df2 Gives Smaller Critical Values
As denominator df grows, the F distribution tightens around its mean and the right tail shrinks. The critical value drops because you need less evidence to reach significance with more data — the within-group variance estimate becomes more reliable.
F-Statistic: What It Measures
The F-statistic is the ratio of between-group variance to within-group variance. An F close to 1 means group means are no more spread out than random chance predicts. A large F means groups differ more than expected — signaling a real effect.