F分布F分布是1924年英国统计学家R·A·Fisher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——α（0.005―0.10）α=0.005Fα k1k21234568 1224∞12345 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 9.419.349.289.23 9.188.838.498.1820000199.049.8026.2818.31 14.4512.4011.0410.119.43 8.918.518.197.927.70 7.517.357.217.096.99 6.896.816.736.666.60 6.546.496.446.40 6.356.075.795.5421615199.247.4724.2616.53 12.9210.889.608.728.08 7.607.236.936.686.48 6.306.166.035.925.82 5.735.655.585.525.46 5.415.365.325.28 5.244.984.734.5022500199.246.1923.1515.56 12.0310.058.817.967.34 6.886.526.236.005.80 5.645.505.375.275.17 5.095.024.954.894.84 4.794.744.704.66 4.624.374.143.9223056199.345.3922.4614.94 11.469.528.307.476.87 6.426.075.795.565.37 5.215.074.964.854.76 4.684.614.544.494.43 4.384.344.304.26 4.233.993.763.5523437199.344.8421.9714.51 11.079.167.957.136.54 6.105.765.485.265.07 4.914.784.664.564.47 4.394.324.264.204.15 4.104.064.023.98 3.953.713.493.2823925199.444.1321.3513.96 10.578.687.506.696.12 5.685.355.084.864.67 4.524.394.284.184.09 4.013.943.883.833.78 3.733.693.653.61 3.583.353.132.9324426199.443.3920.7013.38 10.038.187.016.235.66 5.244.914.644.434.25 4.103.973.863.763.68 3.603.543.473.423.37 3.333.283.253.21 3.182.952.742.5424940199.542.6220.0312.78 9.477.656.505.735.17 4.764.434.173.963.79 3.643.513.403.313.22 3.153.083.022.972.92 2.872.832.792.76 2.732.502.292.0925465199.541.8319.3212.14 8.887.085.955.194.64 4.233.903.653.443.26 3.112.982.872.782.69 2.612.552.482.432.38 2.332.292.252.21 2.181.931.691.43α=0.01 Fα k1k2 12345681224∞12345 67891011121314151617181920212223242526272829304060120∞405298.4934.1221.2016.26 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.。