Hypothesis Testing

F-Table

Find the critical F-value for your numerator and denominator degrees of freedom, at a significance level you choose.

Significance level (α, right-tail area)

Critical F-values at α = 0.05 — columns: numerator df (df₁), rows: denominator df (df₂)

df₂ \ df₁	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120
1	161.45	199.5	215.71	224.58	230.16	233.99	236.77	238.88	240.54	241.88	243.91	245.95	248.01	249.05	250.1	251.14	252.2	253.25
2	18.51	19	19.16	19.25	19.3	19.33	19.35	19.37	19.38	19.4	19.41	19.43	19.45	19.45	19.46	19.47	19.48	19.49
3	10.13	9.55	9.28	9.12	9.01	8.94	8.89	8.85	8.81	8.79	8.74	8.7	8.66	8.64	8.62	8.59	8.57	8.55
4	7.71	6.94	6.59	6.39	6.26	6.16	6.09	6.04	6	5.96	5.91	5.86	5.8	5.77	5.75	5.72	5.69	5.66
5	6.61	5.79	5.41	5.19	5.05	4.95	4.88	4.82	4.77	4.74	4.68	4.62	4.56	4.53	4.5	4.46	4.43	4.4
6	5.99	5.14	4.76	4.53	4.39	4.28	4.21	4.15	4.1	4.06	4	3.94	3.87	3.84	3.81	3.77	3.74	3.7
7	5.59	4.74	4.35	4.12	3.97	3.87	3.79	3.73	3.68	3.64	3.57	3.51	3.44	3.41	3.38	3.34	3.3	3.27
8	5.32	4.46	4.07	3.84	3.69	3.58	3.5	3.44	3.39	3.35	3.28	3.22	3.15	3.12	3.08	3.04	3.01	2.97
9	5.12	4.26	3.86	3.63	3.48	3.37	3.29	3.23	3.18	3.14	3.07	3.01	2.94	2.9	2.86	2.83	2.79	2.75
10	4.96	4.1	3.71	3.48	3.33	3.22	3.14	3.07	3.02	2.98	2.91	2.85	2.77	2.74	2.7	2.66	2.62	2.58
11	4.84	3.98	3.59	3.36	3.2	3.09	3.01	2.95	2.9	2.85	2.79	2.72	2.65	2.61	2.57	2.53	2.49	2.45
12	4.75	3.89	3.49	3.26	3.11	3	2.91	2.85	2.8	2.75	2.69	2.62	2.54	2.51	2.47	2.43	2.38	2.34
13	4.67	3.81	3.41	3.18	3.03	2.92	2.83	2.77	2.71	2.67	2.6	2.53	2.46	2.42	2.38	2.34	2.3	2.25
14	4.6	3.74	3.34	3.11	2.96	2.85	2.76	2.7	2.65	2.6	2.53	2.46	2.39	2.35	2.31	2.27	2.22	2.18
15	4.54	3.68	3.29	3.06	2.9	2.79	2.71	2.64	2.59	2.54	2.48	2.4	2.33	2.29	2.25	2.2	2.16	2.11
16	4.49	3.63	3.24	3.01	2.85	2.74	2.66	2.59	2.54	2.49	2.42	2.35	2.28	2.24	2.19	2.15	2.11	2.06
17	4.45	3.59	3.2	2.96	2.81	2.7	2.61	2.55	2.49	2.45	2.38	2.31	2.23	2.19	2.15	2.1	2.06	2.01
18	4.41	3.55	3.16	2.93	2.77	2.66	2.58	2.51	2.46	2.41	2.34	2.27	2.19	2.15	2.11	2.06	2.02	1.97
19	4.38	3.52	3.13	2.9	2.74	2.63	2.54	2.48	2.42	2.38	2.31	2.23	2.16	2.11	2.07	2.03	1.98	1.93
20	4.35	3.49	3.1	2.87	2.71	2.6	2.51	2.45	2.39	2.35	2.28	2.2	2.12	2.08	2.04	1.99	1.95	1.9
24	4.26	3.4	3.01	2.78	2.62	2.51	2.42	2.36	2.3	2.25	2.18	2.11	2.03	1.98	1.94	1.89	1.84	1.79
30	4.17	3.32	2.92	2.69	2.53	2.42	2.33	2.27	2.21	2.16	2.09	2.01	1.93	1.89	1.84	1.79	1.74	1.68
40	4.08	3.23	2.84	2.61	2.45	2.34	2.25	2.18	2.12	2.08	2	1.92	1.84	1.79	1.74	1.69	1.64	1.58
60	4	3.15	2.76	2.53	2.37	2.25	2.17	2.1	2.04	1.99	1.92	1.84	1.75	1.7	1.65	1.59	1.53	1.47
120	3.92	3.07	2.68	2.45	2.29	2.18	2.09	2.02	1.96	1.91	1.83	1.75	1.66	1.61	1.55	1.5	1.43	1.35

Find the numerator degrees of freedom (df₁, the larger variance or the between-groups df) along the top, and the denominator degrees of freedom (df₂, the smaller variance or the within-groups df) down the side. Reject H₀ if your F statistic exceeds the tabled value.

How to use this tool

Choose your significance level (commonly 0.05).
Find the numerator degrees of freedom (df1) along the top; for one-way ANOVA this is the number of groups minus one.
Find the denominator degrees of freedom (df2) down the side; for one-way ANOVA this is the total sample size minus the number of groups.
Read the critical value where the row and column meet, and compare it with your calculated F statistic.

Formula Reference

One-way ANOVA df1

df1 = k - 1 (k = number of groups)

One-way ANOVA df2

df2 = N - k (N = total sample size)

Regression F-test df

df1 = number of predictors, df2 = n - p - 1

ArticleANOVA: Comparing Three or More Group Means ArticleThe F-Test for Regression ArticleThe F-Distribution CalcANOVA Calculator CalcMultiple Regression Calculator GlossaryGlossary: F-Distribution

Frequently Asked Questions

Which degrees of freedom is df1 and which is df2?+

df1 is the numerator degrees of freedom, associated with the effect being tested (such as between-groups variance in ANOVA). df2 is the denominator degrees of freedom, associated with the error or within-groups variance. Order matters: F(3, 20) is not the same as F(20, 3).

Why is the table one-sided?+

Because the F distribution is only defined for positive values and most F-tests, including ANOVA and the overall regression F-test, ask whether the explained variance is larger than the unexplained variance, a one-directional question.

What if my df2 is not in the table?+

Use the next smaller df2 listed for a slightly more conservative (larger) critical value, or compute the exact value with the ANOVA Calculator or Multiple Regression Calculator.

How is the F-table related to the t-table?+

For a two-tailed t-test, the square of the critical t-value equals the critical F-value with df1 = 1 and the same denominator degrees of freedom.

df₂ \ df₁

120

161.45

199.5

215.71

224.58

230.16

233.99

236.77

238.88

240.54

241.88

243.91

245.95

248.01

249.05

250.1

251.14

252.2

253.25

18.51

19.16

19.25

19.3

19.33

19.35

19.37

19.38

19.4

19.41

19.43

19.45

19.46

19.47

19.48

19.49

10.13

9.55

9.28

9.12

9.01

8.94

8.89

8.85

8.81

8.79

8.74

8.7

8.66

8.64

8.62

8.59

8.57

8.55

7.71

6.94

6.59

6.39

6.26

6.16

6.09

6.04

5.96

5.91

5.86

5.8

5.77

5.75

5.72

5.69

5.66

6.61

5.79

5.41

5.19

5.05

4.95

4.88

4.82

4.77

4.74

4.68

4.62

4.56

4.53

4.5

4.46

4.43

4.4

5.99

5.14

4.76

4.53

4.39

4.28

4.21

4.15

4.1

4.06

3.94

3.87

3.84

3.81

3.77

3.74

3.7

5.59

4.74

4.35

4.12

3.97

3.87

3.79

3.73

3.68

3.64

3.57

3.51

3.44

3.41

3.38

3.34

3.3

3.27

5.32

4.46

4.07

3.84

3.69

3.58

3.5

3.44

3.39

3.35

3.28

3.22

3.15

3.12

3.08

3.04

3.01

2.97

5.12

4.26

3.86

3.63

3.48

3.37

3.29

3.23

3.18

3.14

3.07

3.01

2.94

2.9

2.86

2.83

2.79

2.75

4.96

4.1

3.71

3.48

3.33

3.22

3.14

3.07

3.02

2.98

2.91

2.85

2.77

2.74

2.7

2.66

2.62

2.58

4.84

3.98

3.59

3.36

3.2

3.09

3.01

2.95

2.9

2.85

2.79

2.72

2.65

2.61

2.57

2.53

2.49

2.45

4.75

3.89

3.49

3.26

3.11

2.91

2.85

2.8

2.75

2.69

2.62

2.54

2.51

2.47

2.43

2.38

2.34

4.67

3.81

3.41

3.18

3.03

2.92

2.83

2.77

2.71

2.67

2.6

2.53

2.46

2.42

2.38

2.34

2.3

2.25

4.6

3.74

3.34

3.11

2.96

2.85

2.76

2.7

2.65

2.6

2.53

2.46

2.39

2.35

2.31

2.27

2.22

2.18

4.54

3.68

3.29

3.06

2.9

2.79

2.71

2.64

2.59

2.54

2.48

2.4

2.33

2.29

2.25

2.2

2.16

2.11

4.49

3.63

3.24

3.01

2.85

2.74

2.66

2.59

2.54

2.49

2.42

2.35

2.28

2.24

2.19

2.15

2.11

2.06

4.45

3.59

3.2

2.96

2.81

2.7

2.61

2.55

2.49

2.45

2.38

2.31

2.23

2.19

2.15

2.1

2.06

2.01

4.41

3.55

3.16

2.93

2.77

2.66

2.58

2.51

2.46

2.41

2.34

2.27

2.19

2.15

2.11

2.06

2.02

1.97

4.38

3.52

3.13

2.9

2.74

2.63

2.54

2.48

2.42

2.38

2.31

2.23

2.16

2.11

2.07

2.03

1.98

1.93

4.35

3.49

3.1

2.87

2.71

2.6

2.51

2.45

2.39

2.35

2.28

2.2

2.12

2.08

2.04

1.99

1.95

1.9

4.26

3.4

3.01

2.78

2.62

2.51

2.42

2.36

2.3

2.25

2.18

2.11

2.03

1.98

1.94

1.89

1.84

1.79

4.17

3.32

2.92

2.69

2.53

2.42

2.33

2.27

2.21

2.16

2.09

2.01

1.93

1.89

1.84

1.79

1.74

1.68

4.08

3.23

2.84

2.61

2.45

2.34

2.25

2.18

2.12

2.08

1.92

1.84

1.79

1.74

1.69

1.64

1.58

3.15

2.76

2.53

2.37

2.25

2.17

2.1

2.04

1.99

1.92

1.84

1.75

1.7

1.65

1.59

1.53

1.47

120

3.92

3.07

2.68

2.45

2.29

2.18

2.09

2.02

1.96

1.91

1.83

1.75

1.66

1.61

1.55

1.5

1.43

1.35

How to use this tool

Choose your significance level (commonly 0.05).

Find the numerator degrees of freedom (df1) along the top; for one-way ANOVA this is the number of groups minus one.

Find the denominator degrees of freedom (df2) down the side; for one-way ANOVA this is the total sample size minus the number of groups.

Read the critical value where the row and column meet, and compare it with your calculated F statistic.

Frequently Asked Questions

Which degrees of freedom is df1 and which is df2?+

Why is the table one-sided?+

What if my df2 is not in the table?+

Use the next smaller df2 listed for a slightly more conservative (larger) critical value, or compute the exact value with the ANOVA Calculator or Multiple Regression Calculator.

How is the F-table related to the t-table?+

For a two-tailed t-test, the square of the critical t-value equals the critical F-value with df1 = 1 and the same denominator degrees of freedom.