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Percentage Points for the Chi-Squared Distribution

Source:
A Dictionary of Statistics

Percentage Points for the Chi-Squared Distribution

If X has a χ2 distribution with ν degrees of freedom, then a tabulated value, x, is such that P(X < x)=p%.

p(%)

ν

Lower tail

Upper tail

0.5

2.5

5

90

95

97.5

99

99.5

99.9

1

0.043927

0.039821

0.023932

2.706

3.841

5.024

6.635

7.879

10.83

2

0.01003

0.05064

0.1026

4.605

5.991

7.378

9.210

10.60

13.82

3

0.07172

0.2158

0.3518

6.251

7.815

9.348

11.34

12.84

16.27

4

0.2070

0.4844

0.7107

7.779

9.488

11.14

13.28

14.86

18.47

5

0.4117

0.8312

1.145

9.236

11.07

12.83

15.09

16.75

20.52

6

0.6757

1.237

1.635

10.64

12.59

14.45

16.81

18.55

22.46

7

0.9893

1.690

2.167

12.02

14.07

16.01

18.48

20.28

24.32

8

1.344

2.180

2.733

13.36

15.51

17.53

20.09

21.95

26.12

9

1.735

2.700

3.325

14.68

16.92

19.02

21.67

23.59

27.88

10

2.156

3.247

3.940

15.99

18.31

20.48

23.21

25.19

29.59

11

2.603

3.816

4.575

17.28

19.68

21.92

24.72

26.76

31.26

12

3.074

4.404

5.226

18.55

21.03

23.34

26.22

28.30

32.91

13

3.565

5.009

5.892

19.81

22.36

24.74

27.69

29.82

34.53

14

4.075

5.629

6.571

21.06

23.68

26.12

29.14

31.32

36.12

15

4.601

6.262

7.261

22.31

25.00

27.49

30.58

32.80

37.70

16

5.142

6.908

7.962

23.54

26.30

28.85

32.00

34.27

39.25

17

5.697

7.564

8.672

24.77

27.59

30.19

33.41

35.72

40.79

18

6.265

8.231

9.390

25.99

28.87

31.53

34.81

37.16

42.31

19

6.844

8.907

10.12

27.20

30.14

32.85

36.19

38.58

43.82

20

7.434

9.591

10.85

28.41

31.41

34.17

37.57

40.00

45.31

21

8.034

10.28

11.59

29.62

32.67

35.48

38.93

41.40

46.80

22

8.643

10.98

12.34

30.81

33.92

36.78

40.29

42.80

48.27

23

9.260

11.69

13.09

32.01

35.17

38.08

41.64

44.18

49.73

24

9.886

12.40

13.85

33.20

36.42

39.36

42.98

45.56

51.18

25

10.52

13.12

14.61

34.38

37.65

40.65

44.31

46.93

52.62

30

13.79

16.79

18.49

40.26

43.77

46.98

50.89

53.67

59.70

40

20.71

24.43

26.51

51.81

55.76

59.34

63.69

66.77

73.40

50

27.99

32.36

34.76

63.17

67.50

71.42

76.15

79.49

86.66

60

35.53

40.48

43.19

74.40

79.08

83.30

88.38

91.95

99.61

70

43.28

48.76

51.74

85.53

90.53

95.02

100.4

104.2

112.3

80

51.17

57.15

60.39

96.58

101.9

106.6

112.3

116.3

124.8

90

59.20

65.65

69.13

107.6

113.1

118.1

124.1

128.3

137.2

100

67.33

74.22

77.93

118.5

124.3

129.6

135.8

140.2

149.4

NB. For values of ν > 100 use the result that √2X has an approximate normal distribution with mean √2ν−1 and variance 1.