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13.4: A | Statistical Table- F Distribution

  • Page ID
    13026
  • \(F\) Distribution

    Figure A1 Table entry for \(p\) is the critical value \(F^{*}\) with probability \(p\) lying to its right.

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 1 2 3 4 5 6 7 8 9
    1 .100 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86
    .050 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54
    .025 647.79 799.50 864.16 899.58 921.85 937.11 948.22 956.66 963.28
    .010 4052.2 4999.5 5403.4 5624.6 5763.6 5859.0 5928.4 5981.1 6022.5
    .001 405284 500000 540379 562500 576405 585937 592873 598144 602284
    2 .100 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38
    .050 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38
    .025 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39
    .010 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39
    .001 998.50 999.00 999.17 999.25 999.30 999.33 999.36 999.37 999.39
    3 .100 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24
    .050 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81
    .025 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47
    .010 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35
    .001 167.03 148.50 141.11 137.10 134.58 132.85 131.58 130.62 129.86
    4 .100 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94
    .050 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00
    .025 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90
    .010 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66
    .001 74.14 61.25 56.18 53.44 51.71 50.53 49.66 49.00 48.47
    5 .100 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32
    .050 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77
    .025 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68
    .010 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16
    .001 47.18 37.12 33.20 31.09 29.75 28.83 28.16 27.65 27.24
    6 .100 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96
    .050 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10
    .025 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52
    .010 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98
    .001 35.51 27.00 23.70 21.92 20.80 20.03 19.46 19.03 18.69
    7 .100 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72
    .050 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68
    .025 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82
    .010 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72
    .001 29.25 21.69 18.77 17.20 16.21 15.52 15.02 14.63 14.33

    Table A1 \(F\) critical values

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 10 12 15 20 25 30 40 50 60 120 1000
    1 .100 60.19 60.71 61.22 61.74 62.05 62.26 62.53 62.69 62.79 63.06 63.30
    .050 241.88 243.91 245.95 248.01 249.26 250.10 251.14 251.77 252.20 253.25 254.19
    .025 968.63 976.71 984.87 993.10 998.08 1001.4 1005.6 1008.1 1009.8 1014.0 1017.7
    .010 6055.8 6106.3 6157.3 6208.7 6239.8 6260.6 6286.8 6302.5 6313.0 6339.4 6362.7
    .001 605621 610668 615764 620908 624017 626099 628712 630285 631337 633972 636301
    2 .100 9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.47 9.47 9.48 9.49
    .050 19.40 19.41 19.43 19.45 19.46 19.46 19.47 19.48 19.48 19.49 19.49
    .025 39.40 39.41 39.43 39.45 39.46 39.46 39.47 39.48 39.48 39.49 39.50
    .010 99.40 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.48 99.49 99.50
    .001 999.40 999.42 999.43 999.45 999.46 999.47 999.47 999.48 999.48 999.49 999.50
    3 .100 5.23 5.22 5.20 5.18 5.17 5.17 5.16 5.15 5.15 5.14 5.13
    .050 8.79 8.74 8.70 8.66 8.63 8.62 8.59 8.58 8.57 8.55 8.53
    .025 14.42 14.34 14.25 14.17 14.12 14.08 14.04 14.01 13.99 13.95 13.91
    .010 27.23 27.05 26.87 26.69 26.58 26.50 26.41 26.35 26.32 26.22 26.14
    .001 129.25 128.32 127.37 126.42 125.84 125.45 124.96 124.66 124.47 123.97 123.53
    4 .100 3.92 3.90 3.87 3.84 3.83 3.82 3.80 3.80 3.79 3.78 3.76
    .050 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.70 5.69 5.66 5.63
    .025 8.84 8.75 8.66 8.56 8.50 8.46 8.41 8.38 8.36 8.31 8.26
    .010 14.55 14.37 14.20 14.02 13.91 13.84 13.75 13.69 13.65 13.56 13.47
    .001 48.05 47.41 46.76 46.10 45.70 45.43 45.09 44.88 44.75 44.40 44.09
    5 .100 3.30 3.27 3.24 3.21 3.19 3.17 3.16 3.15 3.14 3.12 3.11
    .050 4.74 4.68 4.62 4.56 4.52 4.50 4.46 4.44 4.43 4.40 4.37
    .025 6.62 6.52 6.43 6.33 6.27 6.23 6.18 6.14 6.12 6.07 6.02
    .010 10.05 9.89 9.72 9.55 9.45 9.38 9.29 9.24 9.20 9.11 9.03
    .001 26.92 26.42 25.91 25.39 25.08 24.87 24.60 24.44 24.33 24.06 23.82
    6 .100 2.94 2.90 2.87 2.84 2.81 2.80 2.78 2.77 2.76 2.74 2.72
    .050 4.06 4.00 3.94 3.87 3.83 3.81 3.77 3.75 3.74 3.70 3.67
    .025 5.46 5.37 5.27 5.17 5.11 5.07 5.01 4.98 4.96 4.90 4.86
    .010 7.87 7.72 7.56 7.40 7.30 7.23 7.14 7.09 7.06 6.97 6.89
    .001 18.41 17.99 17.56 17.12 16.85 16.67 16.44 16.31 16.21 15.98 15.77
    7 .100 2.70 2.67 2.63 2.59 2.57 2.56 2.54 2.52 2.51 2.49 2.47
    .050 3.64 3.57 3.51 3.44 3.40 3.38 3.34 3.32 3.30 3.27 3.23
    .025 4.76 4.67 4.57 4.47 4.40 4.36 4.31 4.28 4.25 4.20 4.15
    .010 6.62 6.47 6.31 6.16 6.06 5.99 5.91 5.86 5.82 5.74 5.66
    .001 14.08 13.71 13.32 12.93 12.69 12.53 12.33 12.20 12.12 11.91 11.72

    Table A2 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 1 2 3 4 5 6 7 8 9
    8 .100 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56
    .050 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39
    .025 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36
    .010 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91
    .001 25.41 18.49 15.83 14.39 13.48 12.86 12.40 12.05 11.77
    9 .100 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44
    .050 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18
    .025 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03
    .010 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35
    .001 22.86 16.39 13.90 12.56 11.71 11.13 10.70 10.37 10.11
    10 .100 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35
    .050 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02
    .025 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78
    .010 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94
    .001 21.04 14.91 12.55 11.28 10.48 9.93 9.52 9.20 8.96
    11 .100 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27
    .050 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90
    .025 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59
    .010 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63
    .001 19.69 13.81 11.56 10.35 9.58 9.05 8.66 8.35 8.12
    12 .100 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21
    .050 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80
    .025 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44
    .010 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39
    .001 18.64 12.97 10.80 9.63 8.89 8.38 8.00 7.71 7.48
    13 .100 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16
    .050 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71
    .025 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31
    .010 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19
    .001 17.82 12.31 10.21 9.07 8.35 7.86 7.49 7.21 6.98
    14 .100 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12
    .050 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65
    .025 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21
    .010 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03
    .001 17.14 11.78 9.73 8.62 7.92 7.44 7.08 6.80 6.58
    15 .100 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09
    .050 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59
    .025 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12
    .010 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89
    .001 16.59 11.34 9.34 8.25 7.57 7.09 6.74 6.47 6.26

    Table A3 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 10 12 15 20 25 30 40 50 60 120 1000
    8 .100 2.54 2.50 2.46 2.42 2.40 2.38 2.36 2.35 2.34 2.32 2.30
    .050 3.35 3.28 3.22 3.15 3.11 3.08 3.04 3.02 3.01 2.97 2.93
    .025 4.30 4.20 4.10 4.00 3.94 3.89 3.84 3.81 3.78 3.73 3.68
    .010 5.81 5.67 5.52 5.36 5.26 5.20 5.12 5.07 5.03 4.95 4.87
    .001 11.54 11.19 10.84 10.48 10.26 10.11 9.92 9.80 9.73 9.53 9.36
    9 .100 2.42 2.38 2.34 2.30 2.27 2.25 2.23 2.22 2.21 2.18 2.16
    .050 3.14 3.07 3.01 2.94 2.89 2.86 2.83 2.80 2.79 2.75 2.71
    .025 3.96 3.87 3.77 3.67 3.60 3.56 3.51 3.47 3.45 3.39 3.34
    .010 5.26 5.11 4.96 4.81 4.71 4.65 4.57 4.52 4.48 4.40 4.32
    .001 9.89 9.57 9.24 8.90 8.69 8.55 8.37 8.26 8.19 8.00 7.84
    10 .100 2.32 2.28 2.24 2.20 2.17 2.16 2.13 2.12 2.11 2.08 2.06
    .050 2.98 2.91 2.85 2.77 2.73 2.70 2.66 2.64 2.62 2.58 2.54
    .025 3.72 3.62 3.52 3.42 3.35 3.31 3.26 3.22 3.20 3.14 3.09
    .010 4.85 4.71 4.56 4.41 4.31 4.25 4.17 4.12 4.08 4.00 3.92
    .001 8.75 8.45 8.13 7.80 7.60 7.47 7.30 7.19 7.12 6.94 6.78
    11 .100 2.25 2.21 2.17 2.12 2.10 2.08 2.05 2.04 2.03 2.00 1.98
    .050 2.85 2.79 2.72 2.65 2.60 2.57 2.53 2.51 2.49 2.45 2.41
    .025 3.53 3.43 3.33 3.23 3.16 3.12 3.06 3.03 3.00 2.94 2.89
    .010 4.54 4.40 4.25 4.10 4.01 3.94 3.86 3.81 3.78 3.69 3.61
    .001 7.92 7.63 7.32 7.01 6.81 6.68 6.52 6.42 6.35 6.18 6.02
    12 .100 2.19 2.15 2.10 2.06 2.03 2.01 1.99 1.97 1.96 1.93 1.91
    .050 2.75 2.69 2.62 2.54 2.50 2.47 2.43 2.40 2.38 2.34 2.30
    .025 3.37 3.28 3.18 3.07 3.01 2.96 2.91 2.87 2.85 2.79 2.73
    .010 4.30 4.16 4.01 3.86 3.76 3.70 3.62 3.57 3.54 3.45 3.37
    .001 7.29 7.00 6.71 6.40 6.22 6.09 5.93 5.83 5.76 5.59 5.44
    13 .100 2.14 2.10 2.05 2.01 1.98 1.96 1.93 1.92 1.90 1.88 1.85
    .050 2.67 2.60 2.53 2.46 2.41 2.38 2.34 2.31 2.30 2.25 2.21
    .025 3.25 3.15 3.05 2.95 2.88 2.84 2.78 2.74 2.72 2.66 2.60
    .010 4.10 3.96 3.82 3.66 3.57 3.51 3.43 3.38 3.34 3.25 3.18
    .001 6.80 6.52 6.23 5.93 5.75 5.63 5.47 5.37 5.30 5.14 4.99
    14 .100 2.10 2.05 2.01 1.96 1.93 1.91 1.89 1.87 1.86 1.83 1.80
    .050 2.60 2.53 2.46 2.39 2.34 2.31 2.27 2.24 2.22 2.18 2.14
    .025 3.15 3.05 2.95 2.84 2.78 2.73 2.67 2.64 2.61 2.55 2.50
    .010 3.94 3.80 3.66 3.51 3.41 3.35 3.27 3.22 3.18 3.09 3.02
    .001 6.40 6.13 5.85 5.56 5.38 5.25 5.10 5.00 4.94 4.77 4.62
    15 .100 2.06 2.02 1.97 1.92 1.89 1.87 1.85 1.83 1.82 1.79 1.76
    .050 2.54 2.48 2.40 2.33 2.28 2.25 2.20 2.18 2.16 2.11 2.07
    .025 3.06 2.96 2.86 2.76 2.69 2.64 2.59 2.55 2.52 2.46 2.40
    .010 3.80 3.67 3.52 3.37 3.28 3.21 3.13 3.08 3.05 2.96 2.88
    .001 6.08 5.81 5.54 5.25 5.07 4.95 4.80 4.70 4.64 4.47 4.33

    Table A4 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 1 2 3 4 5 6 7 8 9
    16 .100 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06
    .050 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54
    .025 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05
    .010 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78
    .001 16.12 10.97 9.01 7.94 7.27 6.80 6.46 6.19 5.98
    17 .100 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03
    .050 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49
    .025 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98
    .010 8.40 6.11 5.19 4.67 4.34 4.10 3.93 3.79 3.68
    .001 15.72 10.66 8.73 7.68 7.02 6.56 6.22 5.96 5.75
    18 .100 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00
    .050 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46
    .025 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93
    .010 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60
    .001 15.38 10.39 8.49 7.46 6.81 6.35 6.02 5.76 5.56
    19 .100 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44
    .050 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18
    .025 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03
    .010 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35
    .001 22.86 16.39 13.90 12.56 11.71 11.13 10.70 10.37 10.11
    20 .100 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96
    .050 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39
    .025 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84
    .010 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46
    .001 14.82 9.95 8.10 7.10 6.46 6.02 5.69 5.44 5.24
    21 .100 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95
    .050 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37
    .025 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80
    .010 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40
    .001 14.59 9.77 7.94 6.95 6.32 5.88 5.56 5.31 5.11
    22 .100 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93
    .050 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34
    .025 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76
    .010 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35
    .001 14.38 9.61 7.80 6.81 6.19 5.76 5.44 5.19 4.99
    23 .100 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92
    .050 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32
    .025 5.75 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73
    .010 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30
    .001 14.20 9.47 7.67 6.70 6.08 5.65 5.33 5.09 4.89

    Table A5 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 10 12 15 20 25 30 40 50 60 120 1000
    16 .100 2.03 1.99 1.94 1.89 1.86 1.84 1.81 1.79 1.78 1.75 1.72
    .050 2.49 2.42 2.35 2.28 2.23 2.19 2.15 2.12 2.11 2.06 2.02
    .025 2.99 2.89 2.79 2.68 2.61 2.57 2.51 2.47 2.45 2.38 2.32
    .010 3.69 3.55 3.41 3.26 3.16 3.10 3.02 2.97 2.93 2.84 2.76
    .001 5.81 5.55 5.27 4.99 4.82 4.70 4.54 4.45 4.39 4.23 4.08
    17 .100 2.00 1.96 1.91 1.86 1.83 1.81 1.78 1.76 1.75 1.72 1.69
    .050 2.45 2.38 2.31 2.23 2.18 2.15 2.10 2.08 2.06 2.01 1.97
    .025 2.92 2.82 2.72 2.62 2.55 2.50 2.44 2.41 2.38 2.32 2.26
    .010 3.59 3.46 3.31 3.16 3.07 3.00 2.92 2.87 2.83 2.75 2.66
    .001 5.58 5.32 5.05 4.78 4.60 4.48 4.33 4.24 4.18 4.02 3.87
    18 .100 1.98 1.93 1.89 1.84 1.80 1.78 1.75 1.74 1.72 1.69 1.66
    .050 2.41 2.34 2.27 2.19 2.14 2.11 2.06 2.04 2.02 1.97 1.92
    .025 2.87 2.77 2.67 2.56 2.49 2.44 2.38 2.35 2.32 2.26 2.20
    .010 3.51 3.37 3.23 3.08 2.98 2.92 2.84 2.78 2.75 2.66 2.58
    .001 5.39 5.13 4.87 4.59 4.42 4.30 4.15 4.06 4.00 3.84 3.69
    19 .100 1.96 1.91 1.86 1.81 1.78 1.76 1.73 1.71 1.70 1.67 1.64
    .050 2.38 2.31 2.23 2.16 2.11 2.07 2.03 2.00 1.98 1.93 1.88
    .025 2.82 2.72 2.62 2.51 2.44 2.39 2.33 2.30 2.27 2.20 2.14
    .010 3.43 3.30 3.15 3.00 2.91 2.84 2.76 2.71 2.67 2.58 2.50
    .001 5.22 4.97 4.70 4.43 4.26 4.14 3.99 3.90 3.84 3.68 3.53
    20 .100 1.94 1.89 1.84 1.79 1.76 1.74 1.71 1.69 1.68 1.64 1.61
    .050 2.35 2.28 2.20 2.12 2.07 2.04 1.99 1.97 1.95 1.90 1.85
    .025 2.77 2.68 2.57 2.46 2.40 2.35 2.29 2.25 2.22 2.16 2.09
    .010 3.37 3.23 3.09 2.94 2.84 2.78 2.69 2.64 2.61 2.52 2.43
    .001 5.08 4.82 4.56 4.29 4.12 4.00 3.86 3.77 3.70 3.54 3.40
    21 .100 1.92 1.87 1.83 1.78 1.74 1.72 1.69 1.67 1.66 1.62 1.59
    .050 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.94 1.92 1.87 1.82
    .025 2.73 2.64 2.53 2.42 2.36 2.31 2.25 2.21 2.18 2.11 2.05
    .010 3.31 3.17 3.03 2.88 2.79 2.72 2.64 2.58 2.55 2.46 2.37
    .001 4.95 4.70 4.44 4.17 4.00 3.88 3.74 3.64 3.58 3.42 3.28
    22 .100 1.90 1.86 1.81 1.76 1.73 1.70 1.67 1.65 1.64 1.60 1.57
    .050 2.30 2.23 2.15 2.07 2.02 1.98 1.94 1.91 1.89 1.84 1.79
    .025 2.70 2.60 2.50 2.39 2.32 2.27 2.21 2.17 2.14 2.08 2.01
    .010 3.26 3.12 2.98 2.83 2.73 2.67 2.58 2.53 2.50 2.40 2.32
    .001 4.83 4.58 4.33 4.06 3.89 3.78 3.63 3.54 3.48 3.32 3.17
    23 .100 1.89 1.84 1.80 1.74 1.71 1.69 1.66 1.64 1.62 1.59 1.55
    .050 2.27 2.20 2.13 2.05 2.00 1.96 1.91 1.88 1.86 1.81 1.76
    .025 2.67 2.57 2.47 2.36 2.29 2.24 2.18 2.14 2.11 2.04 1.98
    .010 3.21 3.07 2.93 2.78 2.69 2.62 2.54 2.48 2.45 2.35 2.27
    .001 4.73 4.48 4.23 3.96 3.79 3.68 3.53 3.44 3.38 3.22 3.08

    Table A6 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 1 2 3 4 5 6 7 8 9
    24 .100 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91
    .050 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30
    .025 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70
    .010 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26
    .001 14.03 9.34 7.55 6.59 5.98 5.55 5.23 4.99 4.80
    25 .100 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89
    .050 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28
    .025 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68
    .010 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22
    .001 13.88 9.22 7.45 6.49 5.89 5.46 5.15 4.91 4.71
    26 .100 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88
    .050 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27
    .025 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65
    .010 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18
    .001 13.74 9.12 7.36 6.41 5.80 5.38 5.07 4.83 4.64
    27 .100 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87
    .050 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25
    .025 5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63
    .010 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15
    .001 13.61 9.02 7.27 6.33 5.73 5.31 5.00 4.76 4.57
    28 .100 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87
    .050 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24
    .025 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61
    .010 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12
    .001 13.50 8.93 7.19 6.25 5.66 5.24 4.93 4.69 4.50
    29 .100 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86
    .050 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22
    .025 5.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59
    .010 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09
    .001 13.39 8.85 7.12 6.19 5.59 5.18 4.87 4.64 4.45
    30 .100 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85
    .050 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21
    .025 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57
    .010 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07
    .001 13.29 8.77 7.05 6.12 5.53 5.12 4.82 4.58 4.39
    40 .100 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79
    .050 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12
    .025 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45
    .010 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89
    .001 12.61 8.25 6.59 5.70 5.13 4.73 4.44 4.21 4.02

    Table A7 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 10 12 15 20 25 30 40 50 60 120 1000
    24 .100 1.88 1.83 1.78 1.73 1.70 1.67 1.64 1.62 1.61 1.57 1.54
    .050 2.25 2.18 2.11 2.03 1.97 1.94 1.89 1.86 1.84 1.79 1.74
    .025 2.64 2.54 2.44 2.33 2.26 2.21 2.15 2.11 2.08 2.01 1.94
    .010 3.17 3.03 2.89 2.74 2.64 2.58 2.49 2.44 2.40 2.31 2.22
    .001 4.64 4.39 4.14 3.87 3.71 3.59 3.45 3.36 3.29 3.14 2.99
    25 .100 1.87 1.82 1.77 1.72 1.68 1.66 1.63 1.61 1.59 1.56 1.52
    .050 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.84 1.82 1.77 1.72
    .025 2.61 2.51 2.41 2.30 2.23 2.18 2.12 2.08 2.05 1.98 1.91
    .010 3.13 2.99 2.85 2.70 2.60 2.54 2.45 2.40 2.36 2.27 2.18
    .001 4.56 4.31 4.06 3.79 3.63 3.52 3.37 3.28 3.22 3.06 2.91
    26 .100 1.86 1.81 1.76 1.71 1.67 1.65 1.61 1.59 1.58 1.54 1.51
    .050 2.22 2.15 2.07 1.99 1.94 1.90 1.85 1.82 1.80 1.75 1.70
    .025 2.59 2.49 2.39 2.28 2.21 2.16 2.09 2.05 2.03 1.95 1.89
    .010 3.09 2.96 2.81 2.66 2.57 2.50 2.42 2.36 2.33 2.23 2.14
    .001 4.48 4.24 3.99 3.72 3.56 3.44 3.30 3.21 3.15 2.99 2.84
    27 .100 1.85 1.80 1.75 1.70 1.66 1.64 1.60 1.58 1.57 1.53 1.50
    .050 2.20 2.13 2.06 1.97 1.92 1.88 1.84 1.81 1.79 1.73 1.68
    .025 2.57 2.47 2.36 2.25 2.18 2.13 2.07 2.03 2.00 1.93 1.86
    .010 3.06 2.93 2.78 2.63 2.54 2.47 2.38 2.33 2.29 2.20 2.11
    .001 4.41 4.17 3.92 3.66 3.49 3.38 3.23 3.14 3.08 2.92 2.78
    28 .100 1.84 1.79 1.74 1.69 1.65 1.63 1.59 1.57 1.56 1.52 1.48
    .050 2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.79 1.77 1.71 1.66
    .025 2.55 2.45 2.34 2.23 2.16 2.11 2.05 2.01 1.98 1.91 1.84
    .010 3.03 2.90 2.75 2.60 2.51 2.44 2.35 2.30 2.26 2.17 2.08
    .001 4.35 4.11 3.86 3.60 3.43 3.32 3.18 3.09 3.02 2.86 2.72
    29 .100 1.83 1.78 1.73 1.68 1.64 1.62 1.58 1.56 1.55 1.51 1.47
    .050 2.18 2.10 2.03 1.94 1.89 1.85 1.81 1.77 1.75 1.70 1.65
    .025 2.53 2.43 2.32 2.21 2.14 2.09 2.03 1.99 1.96 1.89 1.82
    .010 3.00 2.87 2.73 2.57 2.48 2.41 2.33 2.27 2.23 2.14 2.05
    .001 4.29 4.05 3.80 3.54 3.38 3.27 3.12 3.03 2.97 2.81 2.66
    30 .100 1.82 1.77 1.72 1.67 1.63 1.61 1.57 1.55 1.54 1.50 1.46
    .050 2.16 2.09 2.01 1.93 1.88 1.84 1.79 1.76 1.74 1.68 1.63
    .025 2.51 2.41 2.31 2.20 2.12 2.07 2.01 1.97 1.94 1.87 1.80
    .010 2.98 2.84 2.70 2.55 2.45 2.39 2.30 2.25 2.21 2.11 2.02
    .001 4.24 4.00 3.75 3.49 3.33 3.22 3.07 2.98 2.92 2.76 2.61
    40 .100 1.76 1.71 1.66 1.61 1.57 1.54 1.51 1.48 1.47 1.42 1.38
    .050 2.08 2.00 1.92 1.84 1.78 1.74 1.69 1.66 1.64 1.58 1.52
    .025 2.39 2.29 2.18 2.07 1.99 1.94 1.88 1.83 1.80 1.72 1.65
    .010 2.80 2.66 2.52 2.37 2.27 2.20 2.11 2.06 2.02 1.92 1.82
    .001 3.87 3.64 3.40 3.14 2.98 2.87 2.73 2.64 2.57 2.41 2.25

    Table A8 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 1 2 3 4 5 6 7 8 9
    50 .100 2.81 2.41 2.20 2.06 1.97 1.90 1.84 1.80 1.76
    .050 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07
    .025 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.38
    .010 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78
    .001 12.22 7.96 6.34 5.46 4.90 4.51 4.22 4.00 3.82
    60 .100 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74
    .050 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04
    .025 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33
    .010 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72
    .001 11.97 7.77 6.17 5.31 4.76 4.37 4.09 3.86 3.69
    100 .100 2.76 2.36 2.14 2.00 1.91 1.83 1.78 1.73 1.69
    .050 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.97
    .025 5.18 3.83 3.25 2.92 2.70 2.54 2.42 2.32 2.24
    .010 6.90 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.59
    .001 11.50 7.41 5.86 5.02 4.48 4.11 3.83 3.61 3.44
    200 .100 2.73 2.33 2.11 1.97 1.88 1.80 1.75 1.70 1.66
    .050 3.89 3.04 2.65 2.42 2.26 2.14 2.06 1.98 1.93
    .025 5.10 3.76 3.18 2.85 2.63 2.47 2.35 2.26 2.18
    .010 6.76 4.71 3.88 3.41 3.11 2.89 2.73 2.60 2.50
    .001 11.15 7.15 5.63 4.81 4.29 3.92 3.65 3.43 3.26
    1000 .100 2.71 2.31 2.09 1.95 1.85 1.78 1.72 1.68 1.64
    .050 3.85 3.00 2.61 2.38 2.22 2.11 2.02 1.95 1.89
    .025 5.04 3.70 3.13 2.80 2.58 2.42 2.30 2.20 2.13
    .010 6.66 4.63 3.80 3.34 3.04 2.82 2.66 2.53 2.43
    .001 10.89 6.96 5.46 4.65 4.14 3.78 3.51 3.30 3.13

    Table A9 \(F\) critical values (continued)

    Degrees of freedom in the numerator
    Degrees of freedom
    in the denominator
    \(p\) 10 12 15 20 25 30 40 50 60 120 1000
    50 .100 1.73 1.68 1.63 1.57 1.53 1.50 1.46 1.44 1.42 1.38 1.33
    .050 2.03 1.95 1.87 1.78 1.73 1.69 1.63 1.60 1.58 1.51 1.45
    .025 2.32 2.22 2.11 1.99 1.92 1.87 1.80 1.75 1.72 1.64 1.56
    .010 2.70 2.56 2.42 2.27 2.17 2.10 2.01 1.95 1.91 1.80 1.70
    .001 3.67 3.44 3.20 2.95 2.79 2.68 2.53 2.44 2.38 2.21 2.05
    60 .100 1.71 1.66 1.60 1.54 1.50 1.48 1.44 1.41 1.40 1.35 1.30
    .050 1.99 1.92 1.84 1.75 1.69 1.65 1.59 1.56 1.53 1.47 1.40
    .025 2.27 2.17 2.06 1.94 1.87 1.82 1.74 1.70 1.67 1.58 1.49
    .010 2.63 2.50 2.35 2.20 2.10 2.03 1.94 1.88 1.84 1.73 1.62
    .001 3.54 3.32 3.08 2.83 2.67 2.55 2.41 2.32 2.25 2.08 1.92
    100 .100 1.66 1.61 1.56 1.49 1.45 1.42 1.38 1.35 1.34 1.28 1.22
    .050 1.93 1.85 1.77 1.68 1.62 1.57 1.52 1.48 1.45 1.38 1.30
    .025 2.18 2.08 1.97 1.85 1.77 1.71 1.64 1.59 1.56 1.46 1.36
    .010 2.50 2.37 2.22 2.07 1.97 1.89 1.80 1.74 1.69 1.57 1.45
    .001 3.30 3.07 2.84 2.59 2.43 2.32 2.17 2.08 2.01 1.83 1.64
    200 .100 1.63 1.58 1.52 1.46 1.41 1.38 1.34 1.31 1.29 1.23 1.16
    .050 1.88 1.80 1.72 1.62 1.56 1.52 1.46 1.41 1.39 1.30 1.21
    .025 2.11 2.01 1.90 1.78 1.70 1.64 1.56 1.51 1.47 1.37 1.25
    .010 2.41 2.27 2.13 1.97 1.87 1.79 1.69 1.63 1.58 1.45 1.30
    .001 3.12 2.90 2.67 2.42 2.26 2.15 2.00 1.90 1.83 1.64 1.43
    1000 .100 1.61 1.55 1.49 1.43 1.38 1.35 1.30 1.27 1.25 1.18 1.08
    .050 1.84 1.76 1.68 1.58 1.52 1.47 1.41 1.36 1.33 1.24 1.11
    .025 2.06 1.96 1.85 1.72 1.64 1.58 1.50 1.45 1.41 1.29 1.13
    .010 2.34 2.20 2.06 1.90 1.79 1.72 1.61 1.54 1.50 1.35 1.16
    .001 2.99 2.77 2.54 2.30 2.14 2.02 1.87 1.77 1.69 1.49 1.22

    Table A10 \(F\) critical values (continued)