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Department of Economics

Statistical Tables for Economists

Index for Statistical Tables

Table

Contents

Page

1

Normal Distribution

1

2

Student-t Distribution

2

3

Chi-Squared Distribution

3

4

F-Distribution ( α = 0. 01)

4-6

5

F-Distribution ( α = 0. 05)

7-9

6

F-Distribution ( α = 0. 10)

10-12

7

Binomial Distribution

13-27

8

Poisson Distribution

28-30

9

Durbin-Watson Critical Values

31

10

Mackinnon's Critical Values

32

11

Johansen Critical Values

33

1

y .2

.3

.4

Table 1: Normal Distribution

0

.1

F(z)

-4

-2

0

z

2

4

Pr ( Z ≤ z) = F ( z) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49

F(z) 0.500 0.504 0.508 0.512 0.516 0.520 0.524 0.528 0.532 0.536 0.540 0.544 0.548 0.552 0.556 0.560 0.564 0.567 0.571 0.575 0.579 0.583 0.587 0.591 0.595 0.599 0.603 0.606 0.610 0.614 0.618 0.622 0.626 0.629 0.633 0.637 0.641 0.644 0.648 0.652 0.655 0.659 0.663 0.666 0.670 0.674 0.677 0.681 0.684 0.688

z 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99

F(z) 0.691 0.695 0.698 0.702 0.705 0.709 0.712 0.716 0.719 0.722 0.726 0.729 0.732 0.736 0.739 0.742 0.745 0.749 0.752 0.755 0.758 0.761 0.764 0.767 0.770 0.773 0.776 0.779 0.782 0.785 0.788 0.791 0.794 0.797 0.800 0.802 0.805 0.808 0.811 0.813 0.816 0.819 0.821 0.824 0.826 0.829 0.831 0.834 0.836 0.839

z 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49

F(z) 0.841 0.844 0.846 0.848 0.851 0.853 0.855 0.858 0.860 0.862 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.883 0.885 0.887 0.889 0.891 0.893 0.894 0.896 0.898 0.900 0.901 0.903 0.905 0.907 0.908 0.910 0.911 0.913 0.915 0.916 0.918 0.919 0.921 0.922 0.924 0.925 0.926 0.928 0.929 0.931 0.932

z 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99

F(z) 0.933 0.934 0.936 0.937 0.938 0.939 0.941 0.942 0.943 0.944 0.945 0.946 0.947 0.948 0.949 0.951 0.952 0.953 0.954 0.954 0.955 0.956 0.957 0.958 0.959 0.960 0.961 0.962 0.962 0.963 0.964 0.965 0.966 0.966 0.967 0.968 0.969 0.969 0.970 0.971 0.971 0.972 0.973 0.973 0.974 0.974 0.975 0.976 0.976 0.977

z 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49

F(z) 0.977 0.978 0.978 0.979 0.979 0.980 0.980 0.981 0.981 0.982 0.982 0.983 0.983 0.983 0.984 0.984 0.985 0.985 0.985 0.986 0.986 0.986 0.987 0.987 0.987 0.988 0.988 0.988 0.989 0.989 0.989 0.990 0.990 0.990 0.990 0.991 0.991 0.991 0.991 0.992 0.992 0.992 0.992 0.992 0.993 0.993 0.993 0.993 0.993 0.994

z 2.50 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99

F(z) 0.994 0.994 0.994 0.994 0.994 0.995 0.995 0.995 0.995 0.995 0.995 0.995 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.999 0.999 0.999

z 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49

F(z) 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

2

.1

y .2

.3

.4

Table 2: Student t-distribution

1-α

0

α -4

-2

0

t(ν,α) 2

4

Pr( X > t ν,α ) = α α

ν 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 60 70 80 90 100

∞

0.10 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.309 1.309 1.308 1.307 1.306 1.303 1.301 1.299 1.296 1.294 1.292 1.291 1.290 1.282

0.05 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.696 1.694 1.692 1.691 1.690 1.684 1.679 1.676 1.671 1.667 1.664 1.662 1.660 1.645

0.025 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.040 2.037 2.035 2.032 2.030 2.021 2.014 2.009 2.000 1.994 1.990 1.987 1.984 1.960

0.01 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.453 2.449 2.445 2.441 2.438 2.423 2.412 2.403 2.390 2.381 2.374 2.368 2.364 2.327

0.005 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.744 2.738 2.733 2.728 2.724 2.704 2.690 2.678 2.660 2.648 2.639 2.632 2.626 2.576

3

.05

y .1

.15

.2

Table 3: Chi-Squared Distribution

1-α 0

α 2

0

χ ν 10

5

15

2 ν, α

Pr( X ≥ χ α

ν 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 60 70 80 90 100

0.995 0.00 0.01 0.07 0.21 0.41 0.68 0.99 1.34 1.73 2.16 2.60 3.07 3.57 4.07 4.60 5.14 5.70 6.26 6.84 7.43 8.03 8.64 9.26 9.89 10.52 11.16 11.81 12.46 13.12 13.79 14.46 15.13 15.82 16.50 17.19 20.71 24.31 27.99 35.53 43.28 51.17 59.20 67.33

0.99 0.00 0.02 0.11 0.30 0.55 0.87 1.24 1.65 2.09 2.56 3.05 3.57 4.11 4.66 5.23 5.81 6.41 7.01 7.63 8.26 8.90 9.54 10.20 10.86 11.52 12.20 12.88 13.56 14.26 14.95 15.66 16.36 17.07 17.79 18.51 22.16 25.90 29.71 37.48 45.44 53.54 61.75 70.06

0.975 0.00 0.05 0.22 0.48 0.83 1.24 1.69 2.18 2.70 3.25 3.82 4.40 5.01 5.63 6.26 6.91 7.56 8.23 8.91 9.59 10.28 10.98 11.69 12.40 13.12 13.84 14.57 15.31 16.05 16.79 17.54 18.29 19.05 19.81 20.57 24.43 28.37 32.36 40.48 48.76 57.15 65.65 74.22

0.95 0.00 0.10 0.35 0.71 1.15 1.64 2.17 2.73 3.33 3.94 4.57 5.23 5.89 6.57 7.26 7.96 8.67 9.39 10.12 10.85 11.59 12.34 13.09 13.85 14.61 15.38 16.15 16.93 17.71 18.49 19.28 20.07 20.87 21.66 22.47 26.51 30.61 34.76 43.19 51.74 60.39 69.13 77.93

0.9 0.02 0.21 0.58 1.06 1.61 2.20 2.83 3.49 4.17 4.87 5.58 6.30 7.04 7.79 8.55 9.31 10.09 10.86 11.65 12.44 13.24 14.04 14.85 15.66 16.47 17.29 18.11 18.94 19.77 20.60 21.43 22.27 23.11 23.95 24.80 29.05 33.35 37.69 46.46 55.33 64.28 73.29 82.36

20

)

0.1 2.71 4.61 6.25 7.78 9.24 10.64 12.02 13.36 14.68 15.99 17.28 18.55 19.81 21.06 22.31 23.54 24.77 25.99 27.20 28.41 29.62 30.81 32.01 33.20 34.38 35.56 36.74 37.92 39.09 40.26 41.42 42.58 43.75 44.90 46.06 51.81 57.51 63.17 74.40 85.53 96.58 107.57 118.50

0.05 3.84 5.99 7.81 9.49 11.07 12.59 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 37.65 38.89 40.11 41.34 42.56 43.77 44.99 46.19 47.40 48.60 49.80 55.76 61.66 67.50 79.08 90.53 101.88 113.15 124.34

0.025 5.02 7.38 9.35 11.14 12.83 14.45 16.01 17.53 19.02 20.48 21.92 23.34 24.74 26.12 27.49 28.85 30.19 31.53 32.85 34.17 35.48 36.78 38.08 39.36 40.65 41.92 43.19 44.46 45.72 46.98 48.23 49.48 50.73 51.97 53.20 59.34 65.41 71.42 83.30 95.02 106.63 118.14 129.56

0.01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 44.31 45.64 46.96 48.28 49.59 50.89 52.19 53.49 54.78 56.06 57.34 63.69 69.96 76.15 88.38 100.43 112.33 124.12 135.81

0.005 7.88 10.60 12.84 14.86 16.75 18.55 20.28 21.95 23.59 25.19 26.76 28.30 29.82 31.32 32.80 34.27 35.72 37.16 38.58 40.00 41.40 42.80 44.18 45.56 46.93 48.29 49.64 50.99 52.34 53.67 55.00 56.33 57.65 58.96 60.27 66.77 73.17 79.49 91.95 104.21 116.32 128.30 140.17

4

y .4

.6

.8

Table 4: F-distribution ( α = 0.01)

.2

α

0

1-α 0

2

Fν1,ν2

4

6

α ν 1, ν 2

Pr( X > F ) = α α = 0.01 ν1

ν2

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 60 120 ∞

4051.3 98.50 34.12 21.20 16.26 13.75 12.25 11.26 10.56 10.04 9.65 9.33 9.07 8.86 8.68 8.53 8.40 8.29 8.18 8.10 8.02 7.95 7.88 7.82 7.77 7.72 7.68 7.64 7.60 7.56 7.53 7.50 7.47 7.44 7.42 7.31 7.23 7.17 7.08 6.85 6.63

4999.5 99.00 30.82 18.00 13.27 10.92 9.55 8.65 8.02 7.56 7.21 6.93 6.70 6.51 6.36 6.23 6.11 6.01 5.93 5.85 5.78 5.72 5.66 5.61 5.57 5.53 5.49 5.45 5.42 5.39 5.36 5.34 5.31 5.29 5.27 5.18 5.11 5.06 4.98 4.79 4.61

5403.5 99.22 29.46 16.69 12.06 9.78 8.45 7.59 6.99 6.55 6.22 5.95 5.74 5.56 5.42 5.29 5.18 5.09 5.01 4.94 4.87 4.82 4.76 4.72 4.68 4.64 4.60 4.57 4.54 4.51 4.48 4.46 4.44 4.42 4.40 4.31 4.25 4.20 4.13 3.95 3.78

5624.8 99.33 28.71 15.98 11.39 9.15 7.85 7.01 6.42 5.99 5.67 5.41 5.21 5.04 4.89 4.77 4.67 4.58 4.50 4.43 4.37 4.31 4.26 4.22 4.18 4.14 4.11 4.07 4.04 4.02 3.99 3.97 3.95 3.93 3.91 3.83 3.77 3.72 3.65 3.48 3.32

5763.9 99.40 28.24 15.52 10.97 8.75 7.46 6.63 6.06 5.64 5.32 5.06 4.86 4.69 4.56 4.44 4.34 4.25 4.17 4.10 4.04 3.99 3.94 3.90 3.85 3.82 3.78 3.75 3.73 3.70 3.67 3.65 3.63 3.61 3.59 3.51 3.45 3.41 3.34 3.17 3.02

5859.2 99.44 27.91 15.21 10.67 8.47 7.19 6.37 5.80 5.39 5.07 4.82 4.62 4.46 4.32 4.20 4.10 4.01 3.94 3.87 3.81 3.76 3.71 3.67 3.63 3.59 3.56 3.53 3.50 3.47 3.45 3.43 3.41 3.39 3.37 3.29 3.23 3.19 3.12 2.96 2.80

5928.6 99.48 27.67 14.98 10.46 8.26 6.99 6.18 5.61 5.20 4.89 4.64 4.44 4.28 4.14 4.03 3.93 3.84 3.77 3.70 3.64 3.59 3.54 3.50 3.46 3.42 3.39 3.36 3.33 3.30 3.28 3.26 3.24 3.22 3.20 3.12 3.07 3.02 2.95 2.79 2.64

5981.3 99.50 27.49 14.80 10.29 8.10 6.84 6.03 5.47 5.06 4.74 4.50 4.30 4.14 4.00 3.89 3.79 3.71 3.63 3.56 3.51 3.45 3.41 3.36 3.32 3.29 3.26 3.23 3.20 3.17 3.15 3.13 3.11 3.09 3.07 2.99 2.94 2.89 2.82 2.66 2.51

6022.7 99.52 27.35 14.66 10.16 7.98 6.72 5.91 5.35 4.94 4.63 4.39 4.19 4.03 3.89 3.78 3.68 3.60 3.52 3.46 3.40 3.35 3.30 3.26 3.22 3.18 3.15 3.12 3.09 3.07 3.04 3.02 3.00 2.98 2.96 2.89 2.83 2.78 2.72 2.56 2.41

6056.1 99.53 27.23 14.55 10.05 7.87 6.62 5.81 5.26 4.85 4.54 4.30 4.10 3.94 3.80 3.69 3.59 3.51 3.43 3.37 3.31 3.26 3.21 3.17 3.13 3.09 3.06 3.03 3.00 2.98 2.96 2.93 2.91 2.89 2.88 2.80 2.74 2.70 2.63 2.47 2.32

5

y .4

.6

.8

Table 4: F-distribution (α = 0.01 ) (cont'd)

.2

α

0

1-α 0

2

Fν1,ν2

4

6

α ν 1, ν 2

Pr( X > F ) = α α = 0.01 ν1

ν2

11

12

13

14

15

16

17

18

19

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 60 120 ∞

6083.6 99.54 27.13 14.45 9.96 7.79 6.54 5.73 5.18 4.77 4.46 4.22 4.02 3.86 3.73 3.62 3.52 3.43 3.36 3.29 3.24 3.18 3.14 3.09 3.06 3.02 2.99 2.96 2.93 2.91 2.88 2.86 2.84 2.82 2.80 2.73 2.67 2.63 2.56 2.40 2.25

6106.6 99.55 27.05 14.37 9.89 7.72 6.47 5.67 5.11 4.71 4.40 4.16 3.96 3.80 3.67 3.55 3.46 3.37 3.30 3.23 3.17 3.12 3.07 3.03 2.99 2.96 2.93 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2.66 2.61 2.56 2.50 2.34 2.18

6126.2 99.56 26.98 14.31 9.82 7.66 6.41 5.61 5.05 4.65 4.34 4.10 3.91 3.75 3.61 3.50 3.40 3.32 3.24 3.18 3.12 3.07 3.02 2.98 2.94 2.90 2.87 2.84 2.81 2.79 2.77 2.74 2.72 2.70 2.69 2.61 2.55 2.51 2.44 2.28 2.13

6142.9 99.57 26.92 14.25 9.77 7.60 6.36 5.56 5.01 4.60 4.29 4.05 3.86 3.70 3.56 3.45 3.35 3.27 3.19 3.13 3.07 3.02 2.97 2.93 2.89 2.86 2.82 2.79 2.77 2.74 2.72 2.70 2.68 2.66 2.64 2.56 2.51 2.46 2.39 2.23 2.08

6157.6 99.58 26.87 14.20 9.72 7.56 6.31 5.52 4.96 4.56 4.25 4.01 3.82 3.66 3.52 3.41 3.31 3.23 3.15 3.09 3.03 2.98 2.93 2.89 2.85 2.81 2.78 2.75 2.73 2.70 2.68 2.65 2.63 2.61 2.60 2.52 2.46 2.42 2.35 2.19 2.04

6170.4 99.58 26.83 14.15 9.68 7.52 6.27 5.48 4.92 4.52 4.21 3.97 3.78 3.62 3.49 3.37 3.27 3.19 3.12 3.05 2.99 2.94 2.89 2.85 2.81 2.78 2.75 2.72 2.69 2.66 2.64 2.62 2.60 2.58 2.56 2.48 2.43 2.38 2.31 2.15 2.00

6181.7 99.59 26.79 14.11 9.64 7.48 6.24 5.44 4.89 4.49 4.18 3.94 3.75 3.59 3.45 3.34 3.24 3.16 3.08 3.02 2.96 2.91 2.86 2.82 2.78 2.75 2.71 2.68 2.66 2.63 2.61 2.58 2.56 2.54 2.53 2.45 2.39 2.35 2.28 2.12 1.97

6191.8 99.59 26.75 14.08 9.61 7.45 6.21 5.41 4.86 4.46 4.15 3.91 3.72 3.56 3.42 3.31 3.21 3.13 3.05 2.99 2.93 2.88 2.83 2.79 2.75 2.72 2.68 2.65 2.63 2.60 2.58 2.55 2.53 2.51 2.50 2.42 2.36 2.32 2.25 2.09 1.93

6200.9 99.60 26.72 14.05 9.58 7.42 6.18 5.38 4.83 4.43 4.12 3.88 3.69 3.53 3.40 3.28 3.19 3.10 3.03 2.96 2.90 2.85 2.80 2.76 2.72 2.69 2.66 2.63 2.60 2.57 2.55 2.53 2.51 2.49 2.47 2.39 2.34 2.29 2.22 2.06 1.90

6209.0 99.60 26.69 14.02 9.55 7.40 6.16 5.36 4.81 4.41 4.10 3.86 3.66 3.51 3.37 3.26 3.16 3.08 3.00 2.94 2.88 2.83 2.78 2.74 2.70 2.66 2.63 2.60 2.57 2.55 2.52 2.50 2.48 2.46 2.44 2.37 2.31 2.27 2.20 2.03 1.88

6

y .4

.6

.8

Table 4: F-distribution (α = 0.01 ) (cont'd)

.2

α

0

1-α 0

Fν1,ν2

2

4

6

α ν 1, ν 2

Pr( X > F ) = α α = 0.01 ν1

ν2

21

22

23

24

25

30

35

40

60

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 60 120 ∞

6216.4 99.60 26.66 13.99 9.53 7.37 6.13 5.34 4.79 4.38 4.08 3.84 3.64 3.48 3.35 3.24 3.14 3.05 2.98 2.92 2.86 2.81 2.76 2.72 2.68 2.64 2.61 2.58 2.55 2.53 2.50 2.48 2.46 2.44 2.42 2.35 2.29 2.24 2.17 2.01 1.85

6223.2 99.61 26.64 13.97 9.51 7.35 6.11 5.32 4.77 4.36 4.06 3.82 3.62 3.46 3.33 3.22 3.12 3.03 2.96 2.90 2.84 2.78 2.74 2.70 2.66 2.62 2.59 2.56 2.53 2.51 2.48 2.46 2.44 2.42 2.40 2.33 2.27 2.22 2.15 1.99 1.83

6229.3 99.61 26.62 13.95 9.49 7.33 6.09 5.30 4.75 4.34 4.04 3.80 3.60 3.44 3.31 3.20 3.10 3.02 2.94 2.88 2.82 2.77 2.72 2.68 2.64 2.60 2.57 2.54 2.51 2.49 2.46 2.44 2.42 2.40 2.38 2.31 2.25 2.20 2.13 1.97 1.81

6234.9 99.61 26.60 13.93 9.47 7.31 6.07 5.28 4.73 4.33 4.02 3.78 3.59 3.43 3.29 3.18 3.08 3.00 2.92 2.86 2.80 2.75 2.70 2.66 2.62 2.58 2.55 2.52 2.49 2.47 2.45 2.42 2.40 2.38 2.36 2.29 2.23 2.18 2.12 1.95 1.79

6240.1 99.61 26.58 13.91 9.45 7.30 6.06 5.26 4.71 4.31 4.01 3.76 3.57 3.41 3.28 3.16 3.07 2.98 2.91 2.84 2.79 2.73 2.69 2.64 2.60 2.57 2.54 2.51 2.48 2.45 2.43 2.41 2.39 2.37 2.35 2.27 2.21 2.17 2.10 1.93 1.77

6261.0 99.62 26.47 13.84 9.38 7.23 5.99 5.20 4.65 4.25 3.94 3.70 3.51 3.35 3.21 3.10 3.00 2.92 2.84 2.78 2.72 2.67 2.62 2.58 2.54 2.50 2.47 2.44 2.41 2.39 2.36 2.34 2.32 2.30 2.28 2.20 2.14 2.10 2.03 1.86 1.70

6275.9 99.63 26.42 13.78 9.33 7.18 5.94 5.15 4.60 4.20 3.89 3.65 3.46 3.30 3.17 3.05 2.96 2.87 2.80 2.73 2.67 2.62 2.57 2.53 2.49 2.45 2.42 2.39 2.36 2.34 2.31 2.29 2.27 2.25 2.23 2.15 2.09 2.05 1.98 1.81 1.64

6287.1 99.63 26.38 13.75 9.29 7.14 5.91 5.12 4.57 4.16 3.86 3.62 3.43 3.27 3.13 3.02 2.92 2.84 2.76 2.69 2.64 2.58 2.54 2.49 2.45 2.42 2.38 2.35 2.33 2.30 2.27 2.25 2.23 2.21 2.19 2.11 2.05 2.01 1.94 1.76 1.59

6313.4 99.64 26.29 13.65 9.20 7.06 5.82 5.03 4.48 4.08 3.78 3.54 3.34 3.18 3.05 2.93 2.83 2.75 2.67 2.61 2.55 2.50 2.45 2.40 2.36 2.33 2.29 2.26 2.23 2.21 2.18 2.16 2.14 2.12 2.10 2.02 1.96 1.91 1.84 1.66 1.47

6339.7 99.65 26.19 13.56 9.11 6.97 5.74 4.95 4.40 4.00 3.69 3.45 3.25 3.09 2.96 2.84 2.75 2.66 2.58 2.52 2.46 2.40 2.35 2.31 2.27 2.23 2.20 2.17 2.14 2.11 2.09 2.06 2.04 2.02 2.00 1.92 1.85 1.80 1.73 1.53 1.32

∞ 6365.9 99.50 26.13 13.46 9.02 6.88 5.65 4.86 4.31 3.91 3.60 3.36 3.17 3.00 2.87 2.75 2.65 2.57 2.49 2.42 2.36 2.31 2.26 2.21 2.17 2.13 2.10 2.06 2.03 2.01 1.98 1.96 1.93 1.91 1.89 1.80 1.74 1.68 1.60 1.38 1.00

7

y .4

.6

.8

Table 5: F-distribution ( α = 0.05)

.2

α

0

1-α 0

1

2

Fν1,ν2

3

4

5

α ν 1, ν 2

Pr( X > F ) = α α = 0.05 ν1

ν2

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 40 45 50 60 120 ∞

161.55 18.51 10.13 7.71 6.61 5.99 5.59 5.32 5.12 4.96 4.84 4.75 4.67 4.60 4.54 4.49 4.45 4.41 4.38 4.35 4.32 4.30 4.28 4.26 4.24 4.23 4.21 4.20 4.18 4.17 4.16 4.15 4.14 4.13 4.12 4.08 4.06 4.03 4.00 3.92 3.84

199.71 19.00 9.55 6.94 5.79 5.14 4.74 4.46 4.26 4.10 3.98 3.89 3.81 3.74 3.68 3.63 3.59 3.55 3.52 3.49 3.47 3.44 3.42 3.40 3.39 3.37 3.35 3.34 3.33 3.32 3.30 3.29 3.28 3.28 3.27 3.23 3.20 3.18 3.15 3.07 3.00

215.95 19.16 9.28 6.59 5.41 4.76 4.35 4.07 3.86 3.71 3.59 3.49 3.41 3.34 3.29 3.24 3.20 3.16 3.13 3.10 3.07 3.05 3.03 3.01 2.99 2.98 2.96 2.95 2.93 2.92 2.91 2.90 2.89 2.88 2.87 2.84 2.81 2.79 2.76 2.68 2.60

224.84 19.25 9.12 6.39 5.19 4.53 4.12 3.84 3.63 3.48 3.36 3.26 3.18 3.11 3.06 3.01 2.96 2.93 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2.73 2...