F分布的概念及表和查表方法(文档)-共6页.pdf

F F 分布分布F 分布是 1924 年英国统计学家 RAFisher 提出，并以其姓氏的第一个字母命名的。它是一种非对称分布，有两个自由度，且位置不可互换。F 分布有着广泛的应用，如在方差分析、回归方程的显著性检验中都有着重要的地位。中文名F 分布外文名F-distribution领 域统计学提出者R.A.Fisher提出时间1924特 性非对称分布目录目录1 定义2 性质定义若总体，与 为来自 X 的两个独立样本，设统计量则称统计量 F 服从自由度 和 的 F 分布，记为 分布的概率密度为 分布的概率密度函数图像如图 1 所示图 1 2若总体 与总体 独立，为来自 X 的一个样本，为来自 Y 的一个样本，则统计量 则称统计量 F 服从自由度为 和 ，非中心参数为 的非中心 F 分布，记为 性质性质性质 1：性质 2：设 ，则 。性质 3：设，则 。性质 4：分布的分布函数可用标准正态分布的分布函数来逼近。即其中，(，充分大)。性质 5：若总体 与 独立，为来自 X 的一个样本，为来自 Y 的一个样本，为已知参数。则统计量 性质 6：若总体 与 独立，为来自 X的一个样本，为来自 Y 的一个样本，则统计量 F 统计学附录表F分布临界值表（0.0050.10）=0.005Fk1k21234568 122412345 67891016211198.555.5531.3322.78 18.6316.2414.6913.6112.83 20000199.049.8026.2818.31 14.4512.4011.0410.119.43 21615199.247.4724.2616.53 12.9210.889.608.728.08 22500199.246.1923.1515.56 12.0310.058.817.967.34 23056199.345.3922.4614.94 11.469.528.307.476.87 23437199.344.8421.9714.51 11.079.167.957.136.54 23925199.444.1321.3513.96 10.578.687.506.696.12 24426199.443.3920.7013.38 10.038.187.016.235.66 24940199.542.6220.0312.78 9.477.656.505.735.17 25465199.541.8319.3212.14 8.887.085.955.194.64 1112131415161718192021222324252627282930406012012.2311.7511.3711.0610.80 10.5810.3810.2210.079.94 9.839.739.639.559.48 9.419.349.289.239.188.838.498.188.918.518.197.927.70 7.517.357.217.096.99 6.896.816.736.666.60 6.546.496.446.406.356.075.795.547.607.236.936.686.48 6.306.166.035.925.82 5.735.655.585.525.46 5.415.365.325.285.244.984.734.506.886.526.236.005.80 5.645.505.375.275.17 5.095.024.954.894.84 4.794.744.704.664.624.374.143.926.426.075.795.565.37 5.215.074.964.854.76 4.684.614.544.494.43 4.384.344.304.264.233.993.763.556.105.765.485.265.07 4.914.784.664.564.47 4.394.324.264.204.15 4.104.064.023.983.953.713.493.285.685.355.084.864.67 4.524.394.284.184.09 4.013.943.883.833.78 3.733.693.653.613.583.353.132.935.244.914.644.434.25 4.103.973.863.763.68 3.603.543.473.423.37 3.333.283.253.213.182.952.742.544.764.434.173.963.79 3.643.513.403.313.22 3.153.083.022.972.92 2.872.832.792.762.732.502.292.094.233.903.653.443.26 3.112.982.872.782.69 2.612.552.482.432.38 2.332.292.252.212.181.931.691.43=0.01 Fk1k2 1234568122412345 678910111213141516171819405298.4934.1221.2016.26 13.7412.2511.2610.5610.04 9.659.339.078.868.68 8.538.408.288.18499999.0130.8118.0013.27 10.929.558.658.027.56 7.206.936.706.516.36 6.236.116.015.93540399.1729.4616.6912.06 9.788.457.596.996.55 6.225.955.745.565.42 5.295.185.095.01562599.2528.7115.9811.39 9.157.857.016.425.99 5.675.415.205.034.89 4.774.674.584.50576499.3028.2415.5210.97 8.757.466.636.065.64 5.325.064.864.694.56 4.444.344.254.17585999.3327.9115.2110.67 8.477.196.375.805.39 5.074.824.624.464.32 4.204.104.013.94598199.3627.4914.8010.29 8.106.846.035.475.06 4.744.504.304.144.00 3.893.793.713.63610699.4227.0514.379.89 7.726.475.675.114.71 4.404.163.963.803.67 3.553.453.373.30623499.4626.6013.939.47 7.316.075.284.734.33 4.023.783.593.433.29 3.183.083.002.92636699.5026.1213.469.02 6.885.654.864.313.91 3.603.363.163.002.87 2.752.652.572.49202122232425262728293040601208.10 8.027.947.887.827.77 7.727.687.647.607.56 7.317.086.856.645.85 5.785.725.665.615.57 5.535.495.455.425.39 5.184.984.794.604.94 4.874.824.764.724.68 4.644.604.574.544.51 4.314.133.953.784.43 4.374.314.264.224.18 4.144.114.074.044.02 3.833.653.483.324.10 4.043.993.943.903.86 3.823.783.753.733.70 3.513.343.173.023.87 3.813.763.713.673.63 3.593.563.533.503.47 3.293.122.962.803.56 3.513.453.413.363.32 3.293.263.233.203.17 2.992.822.662.513.23 3.173.123.073.032.99 2.962.932.902.872.84 2.662.502.342.182.86 2.802.752.702.662.62 2.582.552.522.492.47 2.292.121.951.792.42 2.362.312.262.212.17 2.132.102.062.032.01 1.801.601.381.00=0.025Fk1k212345 6812241234567891011121314151617181920 212223647.838.5117.4412.2210.01 8.818.077.577.216.946.726.556.416.306.20 6.126.045.985.925.87 5.835.795.75799.539.0016.0410.658.43 7.266.546.065.715.465.265.104.974.864.77 4.694.624.564.514.46 4.424.384.35864.239.1715.449.987.76 6.605.895.425.084.834.634.474.354.244.15 4.084.013.953.903.86 3.823.783.75899.639.2515.109.607.39 6.235.525.054.724.474.284.124.003.893.80 3.733.663.613.563.51 3.483.443.41921.839.3014.889.367.15 5.995.294.824.484.244.043.893.773.663.58 3.503.443.383.333.29 3.253.223.18937.139.3314.739.206.98 5.825.124.654.324.073.883.733.603.503.41 3.343.283.223.173.13 3.093.053.02956.739.3714.548.986.76 5.604.904.434.103.853.663.513.393.293.20 3.123.063.012.962.91 2.872.842.81976.739.4114.348.756.52 5.374.674.203.873.623.433.283.153.052.96 2.892.822.772.722.68 2.642.602.57997.239.4614.128.516.28 5.124.423.953.613.373.173.022.892.792.70 2.632.562.502.452.41 2.372.332.30101839.5013.908.266.02 4.854.143.673.333.082.882.722.602.492.40 2.322.252.192.132.09 2.042.001.97=0.05Fk1 k21234568122412345 67161.418.5110.137.716.61 5.995.59199.519.009.556.945.79 5.144.74215.719.169.286.595.41 4.764.35224.619.259.126.395.19 4.534.12230.219.309.016.265.05 4.393.97234.019.338.946.164.95 4.283.87238.919.378.846.044.82 4.153.73243.919.418.745.914.68 4.003.57249.019.458.645.774.53 3.843.41254.319.508.535.634.36 3.673.2324252627282930 40601205.725.69 5.665.635.615.595.57 5.425.295.155.024.324.29 4.274.244.224.204.18 4.053.933.803.693.723.69 3.673.653.633.613.59 3.463.343.233.123.383.35 3.333.313.293.273.25 3.133.012.892.793.153.13 3.103.083.063.043.03 2.902.792.672.572.992.97 2.942.922.902.882.87 2.742.632.522.412.782.75 2.732.712.692.672.65 2.532.412.302.192.542.51 2.492.472.452.432.41 2.292.172.051.94 2.272.24 2.222.192.172.152.14 2.011.881.761.641.941.91 1.881.851.831.811.79 1.641.481.311.008 91011121314151617181920212223242526272829305.325.124.96 4.844.754.674.604.54 4.494.454.414.384.354.324.304.284.264.24 4.224.214.204.184.174.464.264.10 3.983.883.803.743.68 3.633.593.553.523.493.473.443.423.403.38 3.373.353.343.333.324.073.863.71 3.593.493.413.343.29 3.243.203.163.133.103.073.053.033.012.99 2.982.962.952.932.923.843.633.48 3.363.263.183.113.06 3.012.962.932.902.872.842.822.802.782.76 2.742.732.712.702.693.693.483.33 3.203.113.022.962.90 2.852.812.772.742.712.682.662.642.622.60 2.592.572.562.542.533.583.373.22 3.093.002.922.852.79 2.742.702.662.632.602.572.552.532.512.49 2.472.462.442.432.423.443.233.07 2.952.852.772.702.64 2.592.552.512.482.452.422.402.382.362.34 2.322.302.292.282.273.283.072.91 2.792.692.602.532.48 2.422.382.342.312.282.252.232.202.182.16 2.152.132.122.102.093.122.902.74 2.612.502.422.352.29 2.242.192.152.112.082.052.032.001.981.96 1.951.931.911.901.892.932.712.54 2.402.302.212.132.07 2.011.961.921.881.841.811.781.761.731.71 1.691.671.651.641.624060120 4.084.003.923.84 3.233.153.072.99 2.842.762.682.60 2.612.522.452.37 2.452.372.292.21 2.342.252.172.09 2.182.102.021.94 2.001.921.831.75 1.791.701.611.52 1.511.391.251.00=0.10Fk1k21234568122412345678910111213141539.868.535.544.544.06 3.783.593.463.363.29 3.233.183.143.103.0749.509.005.464.323.78 3.463.263.113.012.92 2.862.812.762.732.7053.599.165.364.193.62 3.293.072.922.812.73 2.662.612.562.522.4955.839.245.324.113.52 3.182.962.812.692.61 2.542.482.432.392.3657.249.295.314.053.45 3.112.882.732.612.52 2.452.392.352.312.2758.209.335.284.013.40 3.052.832.672.552.46 2.392.332.282.242.2159.449.375.253.953.34 2.982.752.592.472.38 2.302.242.202.152.1260.719.415.223.903.27 2.902.672.502.382.28 2.212.152.102.052.0262.009.455.183.833.19 2.822.582.402.282.18 2.102.041.981.941.9063.339.495.133.763.10 2.722.472.292.162.06 1.971.901.851.801.761617181920212223242526272829304060120 3.053.033.012.992.97 2.962.952.942.932.92 2.912.902.892.892.88 2.842.792.752.71 2.672.642.622.612.59 2.572.562.552.542.53 2.522.512.502.502.49 2.442.392.352.30 2.462.442.422.402.38 2.362.352.342.332.32 2.312.302.292.282.28 2.232.182.132.08 2.332.312.292.272.25 2.232.222.212.192.18 2.172.172.162.152.14 2.092.041.991.94 2.242.222.202.182.16 2.142.132.112.102.09 2.082.072.062.062.05 2.001.951.901.85 2.182.152.132.112.09 2.082.062.052.042.02 2.012.002.001.991.98 1.931.871.821.17 2.092.062.042.022.00 1.981.971.951.941.93 1.921.911.901.891.88 1.831.771.721.67 1.991.961.931.911.89 1.871.861.841.831.82 1.811.801.791.781.77 1.711.661.601.55 1.871.841.811.791.77 1.751.731.721.701.69 1.681.671.661.651.64 1.571.511.451.38 1.721.691.661.631.61 1.591.571.551.531.52 1.501.491.481.471.46 1.381.291.191.00注：三大抽样分布一般是指卡方分布（2分布）、t 分布和 F 分布，是来自正态总体的三个常用的分布。说明：F 分布表横坐标是 x，纵坐标是 y（如下图），一个 分位点一张表，根据公式中的分子自由度(表第一行数字，k1)和分母自由度（表第一列数字,k2）；它是一种非对称分布，有两个自由度，且位置不可互换。f f 分布表查询方法分布表查询方法例：1.首先需要了解自由度是多少，例如当分位数=0.1 时，找到=0.1 的表。2、这里以分位数为=0.10，自由度为（2,3）的 F 分布为例。首先选择分位数为 0.10 的分位数表，然后找到上方一行的 2，对应 2 下方的一列。3.其次找到左侧一列中的 3，对应 3 的那一行。4.两者相交的那个数字就是需要查找的分位数为 0.10，自由度为（2,3）的 F 分布的值，即 5.46。