An F table (also called the F distribution table, F test table, or F statistic table) is a statistical reference chart listing critical values for right-tailed F-tests. To use it: (1) choose your significance level α, (2) locate numerator degrees of freedom df1 in the columns, (3) locate denominator degrees of freedom df2 in the rows, (4) read the critical value at the intersection. If your F-statistic exceeds this value, your result is statistically significant.

What is the F table used for in ANOVA?

In a one-way ANOVA, the F table gives the critical value to compare against your F-statistic. The numerator df equals the number of groups minus 1 (k − 1). The denominator df equals total observations minus the number of groups (N − k). If F-calculated exceeds F-critical, at least one group mean differs significantly from the others.

What are degrees of freedom in an F table?

The F distribution needs two degrees of freedom: numerator df (df1), based on the number of groups or predictors, and denominator df (df2), based on sample size minus the number of groups. For one-way ANOVA: df1 = k − 1 and df2 = N − k. For regression: df1 = number of predictors and df2 = n − k − 1.

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 for each tail. Look up the upper critical value F(df1, df2) in the α = 0.025 table. The lower critical value equals 1 divided by F(df2, df1) — the reciprocal with the degrees of freedom swapped. Reject H₀ if your F-statistic is above the upper or below the lower critical value.

What is the difference between F table α = 0.05 and α = 0.01?

The α = 0.01 table has higher critical values because stronger evidence is required to reject the null hypothesis. 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 but increase the risk of missing real effects.

How do I find the F table at α = 0.025?

The F table at α = 0.025 is used for two-tailed F-tests where you need the upper critical value at the 2.5% tail. Use the α = 0.025 tab on this page's interactive table. For example, at df1 = 5 and df2 = 20, the F critical value at α = 0.025 is approximately 3.29. This table is also used when your stated α = 0.05 but you're running a two-tailed variance equality test — you split α in half.

Is F = t² always true?

Only when df1 = 1. An F-test with one numerator degree of freedom equals the square of the corresponding t-statistic: F(1, df) = t²(df). For ANOVA with three or more groups, the F-test has no t-test equivalent.

What does a significant F-test in ANOVA mean?

A significant F-test means at least one group mean differs from the others — it does not identify which groups differ. Follow up with post-hoc tests such as Tukey's HSD, Bonferroni correction, or Scheffé's method to pinpoint specific pairwise differences.

F Table | Critical Values for ANOVA (α = 0.05 & 0.01)

Q: How do you read the F table for ANOVA?

For one-way ANOVA: calculate df1 = k − 1 (number of groups minus 1) and df2 = N − k (total observations minus number of groups). Select the α = 0.05 table. Find df1 in the columns and df2 in the rows. The cell at their intersection is the F critical value. If your ANOVA F-statistic is greater than or equal to this value, at least one group mean differs significantly. Example: 3 groups, 30 total observations → df1=2, df2=27, F critical = 3.35 at α=0.05.

Q: How do you find the critical F-value for a right-tailed test?

To find the critical F-value for a right-tailed test: (1) Identify your significance level α (e.g., α = 0.05 or α = 0.10). (2) Calculate numerator df (df1) and denominator df (df2) based on your test type. (3) Use the F table for the right tail — find df1 in the columns and df2 in the rows. (4) The intersection value is the critical F. Example: right-tailed test with α = 0.10, df1 = 1, df2 = 4 → F critical ≈ 4.545. Reject H₀ if your calculated F-statistic exceeds this value.

Q: What is the F critical value at df1=3, df2=30, α=0.05?

The F critical value for F(3, 30) at α = 0.05 is 2.92. Any calculated F-statistic equal to or greater than 2.92 is statistically significant at the 5% significance level and you reject the null hypothesis.

Q: How do you find the p-value from an F table?

The F table gives critical values, not exact p-values. To bracket the p-value: compare your F-statistic across the α = 0.10, 0.05, 0.025, and 0.01 tables for your df1 and df2. If your F falls between the α = 0.05 and α = 0.01 critical values, then 0.01 < p < 0.05. For the exact p-value use Excel: =F.DIST.RT(f_stat, df1, df2).

F Table Quick Reference — Most Common Critical Values

Right-tail critical values at α = 0.05 — the most commonly used significance level.

F(1,10) α=0.05

4.965

df1=1, df2=10

F(2,27) α=0.05

3.354

3 groups, 30 obs

F(3,27) α=0.05

2.960

4 groups, 31 obs

F(3,30) α=0.05

2.922

Most referenced

F(2,30) α=0.05

3.316

Common ANOVA

F(4,45) α=0.05

2.579

Regression

Finding the Critical F-Value for a Right-Tailed Test

To find the critical F-value for a right-tailed test given a significance level (α) and degrees of freedom: (1) Select the table tab for your α below. (2) Find your numerator df (dfᵣ) in the column headers. (3) Find your denominator df (dfᵤ) in the left column. (4) The cell at their intersection is the F critical value.

Common exam example: Right-tailed test at α = 0.10, dfᵣ = 1, dfᵤ = 4 → F critical ≈ 4.545. Use the calculator below for any combination.

F Critical Value Calculator

Numerator df (df₁)

Denominator df (df₂)

Significance Level (α)

F critical value

—

df₂ \ df₁	1	2	3	4	5	6	7	8	10	12	15	20	30

All values are right-tail critical values F_α,(df1,df2). Columns = numerator df₁, Rows = denominator df₂. Click any cell to highlight.

F Distribution Table (F Test Table)

The F distribution table — also called the F test table, F statistic table, or Fisher distribution table — lists critical values of the F distribution defined by two parameters: numerator degrees of freedom (df₁) and denominator degrees of freedom (df₂). Unlike the t-table or chi-square table, you need both df values to look up an F critical value.

What the F Distribution Measures

The F-statistic is the ratio of between-group variance to within-group variance. An F close to 1 means no systematic effect. A large F means groups differ more than random chance predicts — indicating a real effect.

Key Properties

F values are always ≥ 0. The distribution is right-skewed, so all F-table values are right-tail critical values. As both df increase, the distribution becomes more symmetric and critical values decrease.

Named After Sir Ronald Fisher

The F distribution was developed by Ronald Fisher in the 1920s. George Snedecor later tabulated it — which is why it's sometimes called Snedecor's F distribution or the variance ratio distribution.

F Table for ANOVA

The F table for ANOVA (analysis of variance) is used to determine whether group means differ significantly. ANOVA computes an F-statistic and you compare it against this table to decide whether to reject H₀.

One-Way ANOVA — Degrees of Freedom

df₁ = k − 1 df₂ = N − k

k = number of groups, N = total observations across all groups

Two-Way ANOVA — Factor A Degrees of Freedom

df₁ = a − 1 df₂ = ab(n − 1)

a = levels of Factor A, b = levels of Factor B, n = observations per cell

ExampleF Table for One-Way ANOVA at α = 0.05

Scenario: Compare exam scores across 3 teaching methods. 10 students per group (k=3, N=30). Find the F critical value at α = 0.05.

df1 = 3−1 = 2

Numerator df

df2 = 30−3 = 27

Denominator df

F critical = 3.354

From F(2,27) at α=0.05

Decision: If ANOVA gives F ≥ 3.354, at least one teaching method produces significantly different scores. Follow up with Tukey's HSD to identify which pairs differ.

For a full walkthrough of the ANOVA procedure, see the One-Way ANOVA Guide. To compute the F-statistic automatically from your data, use the ANOVA Calculator.

How to Read an F Table: 4 Steps

1 Choose your significance level (α). The most common is α = 0.05. Select that table tab above. Stricter research uses α = 0.01; two-tailed variance tests typically use α = 0.025.

2 Find numerator df (df₁) in the column headers. For ANOVA, df₁ = k − 1 where k is the number of groups. For regression, df₁ is the number of predictors.

3 Find denominator df (df₂) in the left column (rows). For ANOVA, df₂ = N − k. For regression, df₂ = n − p − 1.

4 Compare your F-statistic to the critical value. If F_calc ≥ F_crit, reject H₀. Example: F(3, 30) at α = 0.05 → critical value = 2.922.

df not listed? Round down to the next lower df — gives a slightly higher (conservative) critical value that controls Type I error. For exact values, use the calculator above or Excel: =F.INV.RT(alpha, df1, df2).

F Table by Significance Level

Each significance level has its own F table. Click the tabs above to switch, or use the descriptions below to choose the right table for your test.

F Table at α = 0.05 (95% Confidence)

The most widely used F table. Standard for ANOVA in academic research, clinical studies, and business analytics. If F_calc ≥ critical value, reject H₀ at 5% significance. Common values: F(2,30) = 3.316, F(3,30) = 2.922, F(4,45) = 2.579.

F Table at α = 0.01 (99% Confidence)

Stricter level used when a false positive would be costly — clinical trials, quality control, regulatory studies. Critical values are higher than the 0.05 table. Example: F(2,30) rises from 3.316 to 5.390. Reduces Type I error at the cost of making it harder to detect true effects.

F Table at α = 0.025 (Two-Tailed Variance Tests)

The F table at α = 0.025 is primarily used for two-tailed F-tests — particularly tests of equality of variance (H₀: σ₁² = σ₂²). When running a two-tailed test at overall α = 0.05, you split α in half: use α/2 = 0.025 per tail. Look up the upper critical value in this table, then find the lower critical value as 1 ÷ F(df₂, df₁). Example: F(5,20) at α = 0.025 ≈ 3.29.

See also: F-Test Guide for the full procedure and F Distribution for the mathematical properties of the distribution.

F Table at α = 0.10 (90% Confidence)

Used in exploratory research, pilot studies, or situations where missing a real effect (Type II error) is more costly than a false positive. Critical values are lower than the 0.05 table — easier to reach significance. Example: F(2,30) drops from 3.316 to 2.489. Less common in published research; most journals require α = 0.05.

How to Find the P-Value from an F Table

The F table gives critical values, not exact p-values. Compare your F-statistic across all four α columns to bracket the p-value.

Example: ANOVA gives F = 4.10 with df₁ = 2, df₂ = 30.

Significance Level (α)	F critical value F(2,30)	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 ✗

Conclusion: 0.025 < p < 0.05. Significant at α = 0.05 but not at α = 0.025.

For the exact p-value: Excel: =F.DIST.RT(4.10, 2, 30) returns 0.0271. R: pf(4.10, 2, 30, lower.tail=FALSE). Python: scipy.stats.f.sf(4.10, 2, 30). See the P-values guide for more.

How to Use the F Table for a Two-Tailed Test

1 Halve the significance level. For a two-tailed test at α = 0.05, use α/2 = 0.025 per tail. Switch to the α = 0.025 tab.

2 Find the upper critical value. F_upper = F(df₁, df₂) at α/2. Place the larger sample variance in the numerator so F ≥ 1.

3 Find the lower critical value. F_lower = 1 ÷ F(df₂, df₁) — the reciprocal with degrees of freedom swapped.

4 Reject H₀ if F_calc ≥ F_upper or F_calc ≤ F_lower.

Degrees of Freedom Calculator for F-Tests

Test Type

F Table Worked Examples

Example 1One-Way ANOVA — Three Teaching Methods

k=3 groups, N=30 total, α=0.05. df₁=2, df₂=27. F critical from table = 3.354. If F≥3.354, at least one group mean differs. Use Tukey's HSD for post-hoc comparisons.

Example 2Multiple Regression F-Test — 4 Predictors, n=50

p=4 predictors, n=50 observations, α=0.05. df₁=4, df₂=45. F critical ≈ 2.579. If F≥2.579, at least one predictor is significant. Full guide: Simple Linear Regression.

Example 3Equality of Variance (Two-Tailed), α=0.05

n₁=21, n₂=16, α=0.05 two-tailed → use α/2=0.025. df₁=20, df₂=15. F_upper(20,15) at α=0.025 ≈ 2.76. F_lower = 1÷F(15,20) ≈ 0.39. Reject H₀ if F≥2.76 or F≤0.39.

F Table vs t-Table vs Chi-Square Table

Feature	F Table	t-Table	Chi-Square Table
Shape	Right-skewed	Symmetric	Right-skewed
Parameters	df₁ and df₂	df only	df only
Primary use	ANOVA, regression	Mean comparison (1–2 groups)	Categorical / goodness-of-fit
Relationship	F(1,df) = t²	t² = F when df₁=1	χ²/df ≈ F

Related: T-Test vs ANOVA — when to use each. For choosing between all test types, see the Statistical Test Selector.

Assumptions of the F-Test

1. Independence

Observations within and between groups must be independent. Repeated-measures designs require a different ANOVA approach.

2. Normality

Each group's data should be approximately normal. Check with a Q-Q plot or Shapiro-Wilk test. The F-test is robust to mild non-normality with large samples.

3. Homogeneity of Variance

Group variances should be equal (homoscedasticity). Test with Levene's or Bartlett's test. If violated, use Welch's ANOVA instead.

Common Mistakes When Using the F Table

Confusing df₁ and df₂. Columns hold numerator df, rows hold denominator df. Swapping gives the wrong critical value.

Reading from the wrong α table. If your study uses α=0.01, reading from the α=0.05 table gives a critical value that is too low.

Stopping at the F-test. A significant ANOVA only tells you that group means differ — not which ones. Always follow up with post-hoc tests. See the Tukey HSD guide.

Rounding df up. When exact df is not in the table, round down to the next lower listed value. Rounding up gives a smaller critical value that inflates Type I error.

Using a one-tailed table for a two-tailed variance test. Always use α/2 per tail for two-tailed tests. Switch to the α=0.025 tab for a two-tailed test at overall α=0.05.

F Critical Values Without a Table

Excel

=F.INV.RT(0.05, 3, 27)
// Returns: 2.9604

R

qf(0.95, df1=3, df2=27)
# Output: 2.960351

Python

from scipy import stats
stats.f.ppf(0.95, 3, 27)
# Output: 2.9604

F Table PDF Download — Free Printable

Download a free printable F table PDF — suitable for exams, coursework, and research. The F distribution table 0.05 PDF is the most commonly requested.

F Table PDF — α = 0.05 Most common · df₁ 1–30 · Printable F Table PDF — α = 0.01 Strict significance · df₁ 1–30 · Printable Complete Bundle PDF α = 0.10, 0.05, 0.025, 0.01 · All levels

Frequently Asked Questions About the F Table

What is an F table?

An F table (also called the F distribution table, F test table, or F statistic table) lists critical values for right-tailed F-tests. Select your α, find df₁ in columns and df₂ in rows, and read the critical value at their intersection. If your F-statistic exceeds this value, the result is statistically significant.

How do you read the F table for ANOVA?

Compute df₁ = k − 1 and df₂ = N − k. Select the α = 0.05 tab. Find your df₁ column and df₂ row. The intersection is F critical. If F_calc ≥ F_crit, reject H₀ and conclude at least one group mean differs. Example: k=3, N=30 → df₁=2, df₂=27 → F critical = 3.354.

How do you find the critical F-value for a right-tailed test?

Use this page's table with your α (e.g., 0.10, 0.05, 0.01). Find df₁ in the columns and df₂ in the rows. The cell at their intersection is the right-tail critical F-value. Reject H₀ if your calculated F-statistic equals or exceeds it. For α = 0.10 with df₁=1, df₂=4, the critical F ≈ 4.545.

What is the F critical value at df1=3, df2=30, α=0.05?

F(3, 30) at α = 0.05 is 2.922. Any F-statistic ≥ 2.922 is statistically significant at the 5% level. Use the calculator at the top to find values for any df combination.

How do you find the p-value from an F table?

The table gives critical values, not exact p-values. Compare your F-statistic against all four α columns. If it falls between the 0.05 and 0.01 critical values, then 0.01 < p < 0.05. For the exact p-value: Excel =F.DIST.RT(f, df1, df2), R pf(f, df1, df2, lower.tail=FALSE), Python scipy.stats.f.sf(f, df1, df2).

How do I use the F table at α = 0.025?

The α = 0.025 F table is used for two-tailed variance equality tests where you split α = 0.05 into two tails of 0.025 each. Look up the upper critical value F(df₁, df₂) in the α = 0.025 tab. The lower critical value is 1 ÷ F(df₂, df₁) from the same table with df swapped. Select the "α = 0.025" tab above.

What does a significant F-test mean?

A significant F-test means at least one group mean differs from the others — it does not specify which ones. Follow up with post-hoc tests: Tukey's HSD, Bonferroni correction, or Scheffé's method.