4
Table Critical values of the Studentized range for multiple comparison Level of significance = 0.01 k 2 2 3 4 5 6 7 8 9 10 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 17.969 6.085 4.501 3.926 3.635 3.460 3.344 3.261 3.199 3.151 3.113 3.081 3.055 3.033 3.014 2.998 2.984 2.971 2.960 2.950 2.941 2.933 2.926 2.919 26.98 8.33 5.91 5.04 4.60 4.34 4.16 4.04 3.95 3.88 3.82 3.77 3.73 3.70 3.67 3.65 3.63 3.61 3.59 3.58 3.56 3.55 3.54 3.53 32.82 9.80 6.82 5.76 5.22 4.90 4.68 4.53 4.41 4.33 4.26 4.20 4.15 4.11 4.08 4.05 4.02 4.00 3.98 3.96 3.94 3.93 3.91 3.90 37.08 10.88 7.50 6.29 5.67 5.30 5.06 4.89 4.76 4.65 4.57 4.51 4.45 4.41 4.37 4.33 4.30 4.28 4.25 4.23 4.21 4.20 4.18 4.17 40.41 11.74 8.04 6.71 6.03 5.63 5.36 5.17 5.02 4.91 4.82 4.75 4.69 4.64 4.59 4.56 4.52 4.49 4.47 4.45 4.43 4.41 4.39 4.37 43.12 12.44 8.48 7.05 6.33 5.90 5.61 5.40 5.24 5.12 5.03 4.95 4.88 4.83 4.78 4.74 4.70 4.67 4.65 4.62 4.60 4.58 4.56 4.54 45.40 13.03 8.85 7.35 6.58 6.12 5.82 5.60 5.43 5.30 5.20 5.12 5.05 4.99 4.94 4.90 4.86 4.82 4.79 4.77 4.74 4.72 4.70 4.68 47.36 13.54 9.18 7.60 6.80 6.32 6.00 5.77 5.59 5.46 5.35 5.27 5.19 5.13 5.08 5.03 4.99 4.96 4.92 4.90 4.87 4.85 4.83 4.81 49.07 13.99 9.46 7.83 6.99 6.49 6.16 5.92 5.74 5.60 5.49 5.39 5.32 5.25 5.20 5.15 5.11 5.07 5.04 5.01 4.98 4.96 4.94 4.92 50.59 14.39 9.72 8.03 7.17 6.65 6.30 6.05 5.87 5.72 5.61 5.51 5.43 5.36 5.31 5.26 5.21 5.17 5.14 5.11 5.08 5.05 5.03 5.01 51.96 14.75 9.95 8.21 7.32 6.79 6.43 6.18 5.98 5.83 5.71 5.61 5.53 5.46 5.40 5.35 5.31 5.27 5.23 5.20 5.17 5.15 5.12 5.10 53.20 15.08 10.15 8.37 7.47 6.92 6.55 6.29 6.09 5.93 5.81 5.71 5.63 5.55 5.49 5.44 5.39 5.35 5.31 5.28 5.25 5.23 5.20 5.18 54.33 15.38 10.35 8.52 7.60 7.03 6.66 6.39 6.19 6.03 5.90 5.80 5.71 5.64 5.57 5.52 5.47 5.43 5.39 5.36 5.33 5.30 5.27 5.25 55.36 15.65 10.52 8.66 7.72 7.14 6.76 6.48 6.28 6.11 5.98 5.88 5.79 5.71 5.65 5.59 5.54 5.50 5.46 5.43 5.40 5.37 5.34 5.32 56.32 15.91 10.69 8.79 7.83 7.24 6.85 6.57 6.36 6.19 6.06 5.95 5.85 5.79 5.72 5.66 5.61 5.57 5.53 5.49 5.46 5.43 5.40 5.38 57.22 16.14 10.84 8.91 7.93 7.34 6.94 6.65 6.44 6.27 6.13 6.02 5.93 5.85 5.78 5.73 5.67 563 5.59 5.55 5.52 5.49 5.46 5.44 58.04 16.37 10.98 9.03 8.03 7.43 7.02 6.73 6.51 6.34 6.20 6.09 5.99 5.91 5.85 5.79 5.73 5.69 5.65 5.61 5.58 5.55 5.52 5.49 58.83 16.57 11.11 9.13 8.12 7.51 7.10 6.80 6.58 6.40 6.27 6.15 6.05 5.97 5.90 5.84 5.79 5.74 5.7 5.66 5.62 5.59 5.57 5.55 59.56 16.77 11.24 9.23 8.21 7.59 7.17 6.87 6.64 6.47 6.33 6.21 6.11 6.03 5.96 5.90 5.84 5.79 5.75 5.71 5.67 5.64 5.62 5.59

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  • Table Critical values of the Studentized range for multiple comparison

    Level of significance = 0.01

    k2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201234

    56789

    1011121314

    1516171819

    2021222324

    17.9696.0854.5013.926

    3.6353.4603.3443.2613.199

    3.1513.1133.0813.0553.033

    3.0142.9982.9842.9712.960

    2.9502.9412.9332.9262.919

    26.988.335.915.04

    4.604.344.164.043.95

    3.883.823.773.733.70

    3.673.653.633.613.59

    3.583.563.553.543.53

    32.829.806.825.76

    5.224.904.684.534.41

    4.334.264.204.154.11

    4.084.054.024.003.98

    3.963.943.933.913.90

    37.0810.887.506.29

    5.675.305.064.894.76

    4.654.574.514.454.41

    4.374.334.304.284.25

    4.234.214.204.184.17

    40.4111.748.046.71

    6.035.635.365.175.02

    4.914.824.754.694.64

    4.594.564.524.494.47

    4.454.434.414.394.37

    43.1212.448.487.05

    6.335.905.615.405.24

    5.125.034.954.884.83

    4.784.744.704.674.65

    4.624.604.584.564.54

    45.4013.038.857.35

    6.586.125.825.605.43

    5.305.205.125.054.99

    4.944.904.864.824.79

    4.774.744.724.704.68

    47.3613.549.187.60

    6.806.326.005.775.59

    5.465.355.275.195.13

    5.085.034.994.964.92

    4.904.874.854.834.81

    49.0713.999.467.83

    6.996.496.165.925.74

    5.605.495.395.325.25

    5.205.155.115.075.04

    5.014.984.964.944.92

    50.5914.399.728.03

    7.176.656.306.055.87

    5.725.615.515.435.36

    5.315.265.215.175.14

    5.115.085.055.035.01

    51.9614.759.958.21

    7.326.796.436.185.98

    5.835.715.615.535.46

    5.405.355.315.275.23

    5.205.175.155.125.10

    53.2015.0810.158.37

    7.476.926.556.296.09

    5.935.815.715.635.55

    5.495.445.395.355.31

    5.285.255.235.205.18

    54.3315.3810.358.52

    7.607.036.666.396.19

    6.035.905.805.715.64

    5.575.525.475.435.39

    5.365.335.305.275.25

    55.3615.6510.528.66

    7.727.146.766.486.28

    6.115.985.885.795.71

    5.655.595.545.505.46

    5.435.405.375.345.32

    56.3215.9110.698.79

    7.837.246.856.576.36

    6.196.065.955.855.79

    5.725.665.615.575.53

    5.495.465.435.405.38

    57.2216.1410.848.91

    7.937.346.946.656.44

    6.276.136.025.935.85

    5.785.735.675635.59

    5.555.525.495.465.44

    58.0416.3710.989.03

    8.037.437.026.736.51

    6.346.206.095.995.91

    5.855.795.735.695.65

    5.615.585.555.525.49

    58.8316.5711.119.13

    8.127.517.106.806.58

    6.406.276.156.055.97

    5.905.845.795.745.7

    5.665.625.595.575.55

    59.5616.7711.249.23

    8.217.597.176.876.64

    6.476.336.216.116.03

    5.965.905.845.795.75

    5.715.675.645.625.59

  • Level of significance = 0.01 ()

    k2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 202526272829

    3031323334

    3536373839

    405060120

    2.9132.9072.9022.8972.892

    2.8882.8842.8812.8772.874

    2.8712.8682.8652.8632.861

    2.8582.8412.8292.8002.772

    3.523.513.513.503.49

    3.493.483.483.473.47

    3.463.463.453.453.44

    3.443.413.403.363.31

    3.893.883.873.863.85

    3.853.833.833.823.82

    3.813.813.803.803.79

    3.793.763.743.683.63

    4.164.144.134.124.11

    4.104.094.094.084.07

    4.074.064.054.054.04

    4.044.003.983.923.86

    4.364.344.334.324.31

    4.304.294.284.274.27

    4.264.254.254.244.24

    4.234.194.164.104.03

    4.524.514.504.484.47

    4.464.454.444.444.43

    4.424.414.414.404.40

    4.394.344.314.244.17

    4.664.654.634.624.61

    4.604.594.584.574.56

    4.554.554.544.534.53

    4.524.474.444.364.29

    4.794.784.764.754.73

    4.724.714.704.694.69

    4.674.664.654.644.64

    4.634.584.554.474.39

    4.904.894.874.864.84

    4.824.824.814.804.79

    4.784.774.764.754.75

    4.734.694.654.564.47

    4.994.974.964.944.93

    4.924.914.894.884.87

    4.864.854.844.844.83

    4.824.764.734.644.55

    5.085.065.3045.035.01

    5.004.994.984.974.96

    4.954.944.934.924.92

    4.904.854.814.714.62

    5.165.145.125.115.09

    5.085.075.065.045.03

    5.025.015.005.004.99

    4.984.924.884.784.68

    5.235.215.195.185.16

    5.155.145.135.115.10

    5.095.085.085.075.06

    5.044.994.944.844.74

    5.305.285.265.245.23

    5.215.205.195.175.16

    5.155.145.145.135.12

    5.115.055.004.904.80

    5.365.345.325.305.29

    5.275.265.245.235.22

    5.215.205.195.185.17

    5.165.105.064.954.85

    5.425.405.385.365.35

    5.335.325.305.295.28

    5.275.265.255.245.23

    5.225.155.115.004.89

    5.485.465.435.425.40

    5.385.375.355.345.33

    5.325.315.305.295.28

    5.275.205.155.044.93

    5.525.505.485.465.44

    5.435.415.405.395.37

    5.365.355.345.335.32

    5.225.245.205.094.97

    5.575.555.535.515.49

    5.475.465.455.445.42

    5.415.405.395.385.37

    5.365.295.245.135.01

  • Level of significance = 0.05

    k2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201234

    56789

    1011121314

    1516171819

    2021222324

    90.02514.0368.2606.511

    5.7025.2434.9494.7454.596

    4.4824.3924.3204.2604.210

    4.1674.1314.0994.0714.045

    4.0244.0043.9863.9703.955

    135.019.0210.628.12

    6.986.335.925.645.43

    5.275.155.054.964.89

    4.844.794.744.704.67

    4.644.614.584.564.55

    164.322.2912.179.17

    7.807.086.546.205.96

    5.775.625.505.405.32

    5.255.195.145.095.05

    5.024.994.964.934.91

    185.624.7213.339.96

    8.427.567.016.626.35

    6.145.975.845.735.63

    5.565.495.435.385.33

    5.295.265.225.205.17

    202.226.6314.2410.58

    8.917.977.376.966.66

    6.436.256.105.985.88

    5.805.725.665.605.55

    5.515.475.435.405.37

    215.828.2015.0011.10

    9.328.327.687.246.91

    6.676.486.326.196.08

    5.995.925.855.795.73

    5.695.655.615.575.54

    227.229.5315.6411.5

    9.678.617.947.477.13

    6.876.676.516.376.26

    6.166.086.015.945.89

    5.845.805.765.725.69

    237.030.6816.2011.93

    9.978.878.177.687.33

    7.056.846.676.536.41

    6.316.226.156.086.02

    5.975.925.885.845.81

    245.631.6916.6912.27

    10.249.108.377.867.49

    7.216.996.816.676.54

    6.446.356.276.206.14

    6.096.046.005.965.92

    253.232.5917.1312.57

    10.489.308.558.037.65

    7.367.136.946.796.66

    6.556.436.386.316.25

    6.196.146.106.066.02

    260.033.4017.5312.84

    10.709.488.718.187.78

    7.497.257.066.906.77

    6.666.566.486.416.34

    6.286.246.196.156.11

    266.234.1317.8913.09

    10.899.658.868.317.91

    7.607.367.177.016.87

    6.766.666.576.506.43

    6.376.326.276.236.19

    271.834.8118.2213.32

    11.089.819.008.448.03

    7.717.467.267.106.96

    6.846.746.666.586.51

    6.456.396.356.306.26

    277.035.4318.5213.53

    11.249.959.128.558.13

    7.817.567.367.197.05

    6.936.826.736.656.58

    6.526.476.426.376.33

    281.836.0018.8113.73

    11.4010.089.248.668.23

    7.917.657.447.277.13

    7.006.906.816.736.65

    6.596.536.486.436.39

    286.336.5319.0713.91

    11.5510.219.358.768.33

    7.997.737.527.357.20

    7.076.976.876.796.72

    6.656.596.546.496.45

    290.437.0319.3214.08

    11.6810.329.468.858.41

    8.087.817.597.427.27

    7.147.036.946.856.78

    6.716.656.606.556.51

    294.337.5019.5514.24

    11.8110.439.558.948.49

    8.157.887.667.487.33

    7.207.097.006.916.84

    6.776.706.656.606.56

    298.037.9519.7714.40

    11.9310.549.659.038.57

    8.237.957.737.557.39

    7.267.157.056.976.89

    6.826.766.706.656.61

  • Level of significance = 0.05 ()

    k2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 202526272829

    3031323334

    3536373839

    405060120

    3.9423.9303.9183.9083.889

    3.8893.8813.8733.8653.859

    3.8523.8463.8413.8353.830

    3.8253.7873.7623.7023.643

    4.524.504.494.474.45

    4.454.444.434.424.41

    4.414.004.394.384.38

    4.374.324.284.204.12

    4.894.874.854.834.80

    4.804.794.784.764.75

    4.744.734.724.724.71

    4.704.644.594.504.40

    5.155.125.105.085.05

    5.055.035.025.014.99

    4.984.974.964.954.94

    4.934.864.824.714.60

    5.345.325.305.285.24

    5.245.225.215.195.18

    5.165.155.145.135.12

    5.115.045.494.874.76

    5.515.495.465.445.40

    5.405.385.375.355.34

    5.335.315.305.295.28

    5.265.195.135.014.88

    5.665.635.615.585.54

    5.545.525.505.485.47

    5.455.445.435.415.40

    5.395.305.255.124.99

    5.785.755.725.705.65

    5.655.635.615.595.58

    5.565.555.545.525.51

    5.505.415.365.215.08

    5.895.865.835.805.76

    5.765.745.725.705.68

    5.675.655.645.625.62

    5.605.515.455.305.16

    5.995.955.935.905.85

    5.855.835.815.795.77

    5.765.745.735.725.70

    5.695.595.535.375.23

    6.076.046.015.985.93

    5.935.915.895.875.86

    5.845.825.815.805.78

    5.765.675.605.445.29

    6.156.126.096.066.01

    6.015.995.975.955.93

    5.915.905.885.875.85

    5.835.745.675.505.35

    6.226.196.166.136.08

    6.086.066.036.015.99

    5.985.965.945.935.91

    5.905.805.735.565.40

    6.296.266.226.196.14

    6.146.126.096.076.05

    6.046.026.005.995.97

    5.965.865.785.615.45

    6.356.326.286.256.20

    6.206.186.166.136.12

    6.106.086.066.056.03

    6.025.915.845.665.49

    6.416.386.346.326.26

    6.266.236.216.196.17

    6.156.136.126.106.08

    6.075.965.895.715.54

    6.476.436.406.376.31

    6.316.296.266.246.22

    6.206.186.176.156.13

    6.126.015.935.755.57

    6.526.486.456.426.32

    6.366.346.316.296.27

    6.256.236.226.206.18

    6.166.065.875.795.61

    6.576.536.506.476.41

    6.416.386.366.346.31

    6.296.286.266.246.23

    6.216.096.015.835.65

    Kanji, Gopal K. 100 Statistical Tests. London : SAGE Publication Ltd., 1993.