F分布的概念及表和查表方法.docx

1、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，

2、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 18.6316.2

3、414.6913.6112.83 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

4、.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.

5、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 5.685.355.0

6、84.864.67 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

7、.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.

8、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 5.184.984.794.60540399.17

9、29.4616.6912.06 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.

10、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

11、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.

12、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 681224123456789101112131415

13、1617181920 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 4.274.2

14、44.224.204.18 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 3.333.313.293.273.2

15、5 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.

16、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 2.292.172.051.94 997.2

17、39.4614.128.516.28 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 k21234568

18、122412345678 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 3.633.593.553.523.493.473.44

19、3.423.403.38 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

20、.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.