F分布的概念及表和查表方法

1、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

2、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

3、60; 。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

4、.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

5、.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  5.41

6、5.365.325.285.244.984.734.5022500199.246.1923.1515.56  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  5.215.074.9

7、64.854.76  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  10.578.687.506.696.1

8、2  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  3.333.283.253.213.182.952.742.54249401

9、99.542.6220.0312.78  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&

10、#160; 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  7.3

11、17.086.856.64499999.0130.8118.0013.27  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  5.295.185.095.014.9

12、4  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

13、.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  3.593.563.533.503.4

14、7  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.

15、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.

16、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  8.818.077.577.216.946.72

17、6.556.416.306.20  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  4.053.933.803.69864.2

18、39.1715.449.987.76  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 

19、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.

20、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

21、.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.

22、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 k21234568122412345 678 91011121314151617181920212223242526272829304060120161.418.5110.137.716.61

23、60; 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&#

24、160; 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  3.012.962.932.902.872.8

25、42.822.802.782.76  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  2.452.372.292.21 234.019.338.946.164.95  4.283.873.583.373.22 

26、; 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.

27、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

28、.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

29、.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&#

30、160; 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.

31、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  1.931.871.8