F分布的概念及表和查表方法

F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12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 6789101112131415161718192021222324252627282930406012016211198.555.5531.3322.78 18.6316.2414.6913.6112.83 12.2311.7511.3711.0610.80 10.5810.3810.2210.079.94 9.839.739.639.559.48 9.419.349.289.239.188.838.498.1820000199.049.8026.2818.31 14.4512.4011.0410.119.43 8.918.518.197.927.70 7.517.357.217.096.99 6.896.816.736.666.60 6.546.496.446.406.356.075.795.5421615199.247.4724.2616.53 12.9210.889.608.728.08 7.607.236.936.686.48 6.306.166.035.925.82 5.735.655.585.525.46 5.415.365.325.285.244.984.734.5022500199.246.1923.1515.56 12.0310.058.817.967.34 6.886.526.236.005.80 5.645.505.375.275.17 5.095.024.954.894.84 4.794.744.704.664.624.374.143.9223056199.345.3922.4614.94 11.469.528.307.476.87 6.426.075.795.565.37 5.215.074.964.854.76 4.684.614.544.494.43 4.384.344.304.264.233.993.763.5523437199.344.8421.9714.51 11.079.167.957.136.54 6.105.765.485.265.07 4.914.784.664.564.47 4.394.324.264.204.15 4.104.064.023.983.953.713.493.2823925199.444.1321.3513.96 10.578.687.506.696.12 5.685.355.084.864.67 4.524.394.284.184.09 4.013.943.883.833.78 3.733.693.653.613.583.353.132.9324426199.443.3920.7013.38 10.038.187.016.235.66 5.244.914.644.434.25 4.103.973.863.763.68 3.603.543.473.423.37 3.333.283.253.213.182.952.742.5424940199.542.6220.0312.78 9.477.656.505.735.17 4.764.434.173.963.79 3.643.513.403.313.22 3.153.083.022.972.92 2.872.832.792.762.732.502.292.0925465199.541.8319.3212.14 8.887.085.955.194.64 4.233.903.653.443.26 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 67891011121314151617181920212223242526272829304060120405298.4934.1221.2016.26 13.7412.2511.2610.5610.04 9.659.339.078.868.68 8.538.408.288.188.10 8.027.947.887.827.77 7.727.687.647.607.56 7.317.086.856.64499999.0130.8118.0013.27 10.929.558.658.027.56 7.206.936.706.516.36 6.236.116.015.935.85 5.785.725.665.615.57 5.535.495.455.425.39 5.184.984.794.60540399.1729.4616.6912.06 9.788.457.596.996.55 6.225.955.745.565.42 5.295.185.095.014.94 4.874.824.764.724.68 4.644.604.574.544.51 4.314.133.953.78562599.2528.7115.9811.39 9.157.857.016.425.99 5.675.415.205.034.89 4.774.674.584.504.43 4.374.314.264.224.18 4.144.114.074.044.02 3.833.653.483.32576499.3028.2415.5210.97 8.757.466.636.065.64 5.325.064.864.694.56 4.444.344.254.174.10 4.043.993.943.903.86 3.823.783.753.733.70 3.513.343.173.02585999.3327.9115.2110.67 8.477.196.375.805.39 5.074.824.624.464.32 4.204.104.013.943.87 3.813.763.713.673.63 3.593.563.533.503.47 3.293.122.962.80598199.3627.4914.8010.29 8.106.846.035.475.06 4.744.504.304.144.00 3.893.793.713.633.56 3.513.453.413.363.32 3.293.263.233.203.17 2.992.822.662.51610699.4227.0514.379.89 7.726.475.675.114.71 4.404.163.963.803.67 3.553.453.373.303.23 3.173.123.073.032.99 2.962.932.902.872.84 2.662.502.342.18623499.4626.6013.939.47 7.316.075.284.734.33 4.023.783.593.433.29 3.183.083.002.922.86 2.802.752.702.662.62 2.582.552.522.492.47 2.292.121.951.79636699.5026.1213.469.02 6.885.654.864.313.91 3.603.363.163.002.87 2.752.652.572.492.42 2.362.312.262.212.17 2.132.102.062.032.01 1.801.601.381.00=0.025Fk1k212345 6812241234567891011121314151617181920 21222324252627282930 4060120647.838.5117.4412.2210.01 8.818.077.577.216.946.726.556.416.306.20 6.126.045.985.925.87 5.835.795.755.725.69 5.665.635.615.595.57 5.425.295.155.02799.539.0016.0410.658.43 7.266.546.065.715.465.265.104.974.864.77 4.694.624.564.514.46 4.424.384.354.324.29 4.274.244.224.204.18 4.053.933.803.69864.239.1715.449.987.76 6.605.895.425.084.834.634.474.354.244.15 4.084.013.953.903.86 3.823.783.753.723.69 3.673.653.633.613.59 3.463.343.233.12899.639.2515.109.607.39 6.235.525.054.724.474.284.124.003.893.80 3.733.663.613.563.51 3.483.443.413.383.35 3.333.313.293.273.25 3.133.012.892.79921.839.3014.889.367.15 5.995.294.824.484.244.043.893.773.663.58 3.503.443.383.333.29 3.253.223.183.153.13 3.103.083.063.043.03 2.902.792.672.57937.139.3314.739.206.98 5.825.124.654.324.073.883.733.603.503.41 3.343.283.223.173.13 3.093.053.022.992.97 2.942.922.902.882.87 2.742.632.522.41956.739.3714.548.986.76 5.604.904.434.103.853.663.513.393.293.20 3.123.063.012.962.91 2.872.842.812.782.75 2.732.712.692.672.65 2.532.412.302.19976.739.4114.348.756.52 5.374.674.203.873.623.433.283.153.052.96 2.892.822.772.722.68 2.642.602.572.542.51 2.492.472.452.432.41 2.292.172.051.94 997.239.4614.128.516.28 5.124.423.953.613.373.173.022.892.792.70 2.632.562.502.452.41 2.372.332.302.272.24 2.222.192.172.152.14 2.011.881.761.64101839.5013.908.266.02 4.854.143.673.333.082.882.722.602.492.40 2.322.252.192.132.09 2.042.001.971.941.91 1.881.851.831.811.79 1.641.481.311.00=0.05Fk1 k21234568122412345678 91011121314151617181920212223242526272829304060120161.418.5110.137.716.61 5.995.595.325.124.96 4.844.754.674.604.54 4.494.454.414.384.354.324.304.284.264.24 4.224.214.204.184.17 4.084.003.923.84199.519.009.556.945.79 5.144.744.464.264.10 3.983.883.803.743.68 3.633.593.553.523.493.473.443.423.403.38 3.373.353.343.333.32 3.233.153.072.99215.719.169.286.595.41 4.764.354.073.863.71 3.593.493.413.343.29 3.243.203.163.133.103.073.053.033.012.99 2.982.962.952.932.92 2.842.762.682.60224.619.259.126.395.19 4.534.123.843.633.48 3.363.263.183.113.06 3.012.962.932.902.872.842.822.802.782.76 2.742.732.712.702.69 2.612.522.452.37230.219.309.016.265.05 4.393.973.693.483.33 3.203.113.022.962.90 2.852.812.772.742.712.682.662.642.622.60 2.592.572.562.542.53 2.452.372.292.21234.019.338.946.164.95 4.283.873.583.373.22 3.093.002.922.852.79 2.742.702.662.632.602.572.552.532.512.49 2.472.462.442.432.42 2.342.252.172.09238.919.378.846.044.82 4.153.733.443.233.07 2.952.852.772.702.64 2.592.552.512.482.452.422.402.382.362.34 2.322.302.292.282.27 2.182.102.021.94243.919.418.745.914.68 4.003.573.283.072.91 2.792.692.602.532.48 2.422.382.342.312.282.252.232.202.182.16 2.152.132.122.102.09 2.001.921.831.75249.019.458.645.774.53 3.843.413.122.902.74 2.612.502.422.352.29 2.242.192.152.112.082.052.032.001.981.96 1.951.931.911.901.89 1.791.701.611.52254.319.508.535.634.36 3.673.232.932.712.54 2.402.302.212.132.07 2.011.961.921.881.841.811.781.761.731.71 1.691.671.651.641.62 1.511.391.251.00=0.10Fk1k212345681224123456789101112131415161718192021222324252627282930406012039.868.535.544.544.06 3.783.593.463.363.29 3.233.183.143.103.07 3.053.033.012.992.97 2.962.952.942.932.92 2.912.902.892.892.88 2.842.792.752.7149.509.005.464.323.78 3.463.263.113.012.92 2.862.812.762.732.70 2.672.642.622.612.59 2.572.562.552.542.53 2.522.512.502.502.49 2.442.392.352.3053.599.165.364.193.62 3.293.072.922.812.73 2.662.612.562.522.49 2.462.442.422.402.38 2.362.352.342.332.32 2.312.302.292.282.28 2.232.182.132.0855.839.245.324.113.52 3.182.962.812.692.61 2.542.482.432.392.36 2.332.312.292.272.25 2.232.222.212.192.18 2.172.172.162.152.14 2.092.041.991.9457.249.295.314.053.45 3.112.882.732.612.52 2.452.392.352.312.27 2.242.222.202.182.16 2.142.132.112.102.09 2.082.072.062.062.05 2.001.951.901.8558.209.335.284.013.40 3.052.832.672.552.46 2.392.332.282.242.21 2.182.152.132.112.09 2.082.062.052.042.02 2.012.002.001.991.98 1.931.871.821.1759.449.375.253.953.34 2.982.752.592.472.38 2.302.242.202.152