2022年F分布的概念及表和查表方法_共6页

1、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 1 2若总体与总体独立，为来自 x 的一个样本，精品学习资料 可选择p d f - - - -

2、- - - - - - - - - - 第 1 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 1 页，共 12 页 - - - - - - - - -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。则统计量精品学习资料 可选择p

3、d f - - - - - - - - - - - - - - 第 2 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 2 页，共 12 页 - - - - - - - - -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（0.005 0.10） =0.005fk1k21234568 12241234567891016211198.555.5531.3322.7818.6316.2414.6913.6112.8320000199.049

4、.8026.2818.3114.4512.4011.0410.119.4321615199.247.4724.2616.5312.9210.889.608.728.0822500199.246.1923.1515.5612.0310.058.817.967.3423056199.345.3922.4614.9411.469.528.307.476.8723437199.344.8421.9714.5111.079.167.957.136.5423925199.444.1321.3513.9610.578.687.506.696.1224426199.443.3920.7013.3810.038

5、.187.016.235.6624940199.542.6220.0312.789.477.656.505.735.1725465199.541.8319.3212.148.887.085.955.194.64精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 3 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 3 页，共 12 页 - - - - - - - - -11121314151617181920212223242526272829304060120

6、12.2311.7511.3711.0610.8010.5810.3810.2210.079.949.839.739.639.559.489.419.349.289.239.188.838.498.188.918.518.197.927.707.517.357.217.096.996.896.816.736.666.606.546.496.446.406.356.075.795.547.607.236.936.686.486.306.166.035.925.825.735.655.585.525.465.415.365.325.285.244.984.734.506.886.526.236.0

7、05.805.645.505.375.275.175.095.024.954.894.844.794.744.704.664.624.374.143.926.426.075.795.565.375.215.074.964.854.764.684.614.544.494.434.384.344.304.264.233.993.763.556.105.765.485.265.074.914.784.664.564.474.394.324.264.204.154.104.064.023.983.953.713.493.285.685.355.084.864.674.524.394.284.184.0

8、94.013.943.883.833.783.733.693.653.613.583.353.132.935.244.914.644.434.254.103.973.863.763.683.603.543.473.423.373.333.283.253.213.182.952.742.544.764.434.173.963.793.643.513.403.313.223.153.083.022.972.922.872.832.792.762.732.502.292.094.233.903.653.443.263.112.982.872.782.692.612.552.482.432.382.3

9、32.292.252.212.181.931.691.43精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 4 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 4 页，共 12 页 - - - - - - - - -=0.01fk1k21234568122412345678910111213141516171819405298.4934.1221.2016.2613.7412.2511.2610.5610.049.659.339.078.868.688.53

10、8.408.288.18499999.0130.8118.0013.2710.929.558.658.027.567.206.936.706.516.366.236.116.015.93540399.1729.4616.6912.069.788.457.596.996.556.225.955.745.565.425.295.185.095.01562599.2528.7115.9811.399.157.857.016.425.995.675.415.205.034.894.774.674.584.50576499.3028.2415.5210.978.757.466.636.065.645.3

11、25.064.864.694.564.444.344.254.17585999.3327.9115.2110.678.477.196.375.805.395.074.824.624.464.324.204.104.013.94598199.3627.4914.8010.298.106.846.035.475.064.744.504.304.144.003.893.793.713.63610699.4227.0514.379.897.726.475.675.114.714.404.163.963.803.673.553.453.373.30623499.4626.6013.939.477.316

12、.075.284.734.334.023.783.593.433.293.183.083.002.92636699.5026.1213.469.026.885.654.864.313.913.603.363.163.002.872.752.652.572.49精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 5 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 5 页，共 12 页 - - - - - - - - -2021222324252627282930

13、40601208.108.027.947.887.827.777.727.687.647.607.567.317.086.856.645.855.785.725.665.615.575.535.495.455.425.395.184.984.794.604.944.874.824.764.724.684.644.604.574.544.514.314.133.953.784.434.374.314.264.224.184.144.114.074.044.023.833.653.483.324.104.043.993.943.903.863.823.783.753.733.703.513.343

14、.173.023.873.813.763.713.673.633.593.563.533.503.473.293.122.962.803.563.513.453.413.363.323.293.263.233.203.172.992.822.662.513.233.173.123.073.032.992.962.932.902.872.842.662.502.342.182.862.802.752.702.662.622.582.552.522.492.472.292.121.951.792.422.362.312.262.212.172.132.102.062.032.011.801.601

15、.381.00=0.025fk1k212345681224精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 6 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 6 页，共 12 页 - - - - - - - - -1234567891011121314151617181920212223647.838.5117.4412.2210.018.818.077.577.216.946.726.556.416.306.206.126.045.985.925.875

16、.835.795.75799.539.0016.0410.658.437.266.546.065.715.465.265.104.974.864.774.694.624.564.514.464.424.384.35864.239.1715.449.987.766.605.895.425.084.834.634.474.354.244.154.084.013.953.903.863.823.783.75899.639.2515.109.607.396.235.525.054.724.474.284.124.003.893.803.733.663.613.563.513.483.443.41921

17、.839.3014.889.367.155.995.294.824.484.244.043.893.773.663.583.503.443.383.333.293.253.223.18937.139.3314.739.206.985.825.124.654.324.073.883.733.603.503.413.343.283.223.173.133.093.053.02956.739.3714.548.986.765.604.904.434.103.853.663.513.393.293.203.123.063.012.962.912.872.842.81976.739.4114.348.7

18、56.525.374.674.203.873.623.433.283.153.052.962.892.822.772.722.682.642.602.57997.239.4614.128.516.285.124.423.953.613.373.173.022.892.792.702.632.562.502.452.412.372.332.30101839.5013.908.266.024.854.143.673.333.082.882.722.602.492.402.322.252.192.132.092.042.001.97精品学习资料 可选择p d f - - - - - - - - -

19、- - - - - 第 7 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 7 页，共 12 页 - - - - - - - - -=0.05fk1 k2123456812241234567161.418.5110.137.716.615.995.59199.519.009.556.945.795.144.74215.719.169.286.595.414.764.35224.619.259.126.395.194.534.12230.219.309.016.265.054.393.97234.01

20、9.338.946.164.954.283.87238.919.378.846.044.824.153.73243.919.418.745.914.684.003.57249.019.458.645.774.533.843.41254.319.508.535.634.363.673.232425262728293040601205.725.695.665.635.615.595.575.425.295.155.024.324.294.274.244.224.204.184.053.933.803.693.723.693.673.653.633.613.593.463.343.233.123.3

21、83.353.333.313.293.273.253.133.012.892.793.153.133.103.083.063.043.032.902.792.672.572.992.972.942.922.902.882.872.742.632.522.412.782.752.732.712.692.672.652.532.412.302.192.542.512.492.472.452.432.412.292.172.051.942.272.242.222.192.172.152.142.011.881.761.641.941.911.881.851.831.811.791.641.481.3

22、11.00精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 8 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 8 页，共 12 页 - - - - - - - - -8 91011121314151617181920212223242526272829305.325.124.964.844.754.674.604.544.494.454.414.384.354.324.304.284.264.244.224.214.204.184.174.464.264.

23、103.983.883.803.743.683.633.593.553.523.493.473.443.423.403.383.373.353.343.333.324.073.863.713.593.493.413.343.293.243.203.163.133.103.073.053.033.012.992.982.962.952.932.923.843.633.483.363.263.183.113.063.012.962.932.902.872.842.822.802.782.762.742.732.712.702.693.693.483.333.203.113.022.962.902.

24、852.812.772.742.712.682.662.642.622.602.592.572.562.542.533.583.373.223.093.002.922.852.792.742.702.662.632.602.572.552.532.512.492.472.462.442.432.423.443.233.072.952.852.772.702.642.592.552.512.482.452.422.402.382.362.342.322.302.292.282.273.283.072.912.792.692.602.532.482.422.382.342.312.282.252.

25、232.202.182.162.152.132.122.102.093.122.902.742.612.502.422.352.292.242.192.152.112.082.052.032.001.981.961.951.931.911.901.892.932.712.542.402.302.212.132.072.011.961.921.881.841.811.781.761.731.711.691.671.651.641.62精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 9 页，共 12 页 - - - - - - - - -精品学习资料 可

26、选择p d f - - - - - - - - - - - - - - 第 9 页，共 12 页 - - - - - - - - -40601204.084.003.923.843.233.153.072.992.842.762.682.602.612.522.452.372.452.372.292.212.342.252.172.092.182.102.021.942.001.921.831.751.791.701.611.521.511.391.251.00=0.10fk1k21234568122412345678910111213141539.868.535.544.544.063.78

27、3.593.463.363.293.233.183.143.103.0749.509.005.464.323.783.463.263.113.012.922.862.812.762.732.7053.599.165.364.193.623.293.072.922.812.732.662.612.562.522.4955.839.245.324.113.523.182.962.812.692.612.542.482.432.392.3657.249.295.314.053.453.112.882.732.612.522.452.392.352.312.2758.209.335.284.013.4

28、03.052.832.672.552.462.392.332.282.242.2159.449.375.253.953.342.982.752.592.472.382.302.242.202.152.1260.719.415.223.903.272.902.672.502.382.282.212.152.102.052.0262.009.455.183.833.192.822.582.402.282.182.102.041.981.941.9063.339.495.133.763.102.722.472.292.162.061.971.901.851.801.76精品学习资料 可选择p d f

29、 - - - - - - - - - - - - - - 第 10 页，共 12 页 - - - - - - - - -精品学习资料 可选择p d f - - - - - - - - - - - - - - 第 10 页，共 12 页 - - - - - - - - -16171819202122232425262728293040601203.053.033.012.992.972.962.952.942.932.922.912.902.892.892.882.842.792.752.712.672.642.622.612.592.572.562.552.542.532.522.512.502.502.492.442.392.352.302.462.442.422.402.382.362.352.342.332.322.312.302.292.282.282.232.182.132.082.332.312.292.272.252.232.222.212.192.182.172.172.162.152.142.092.041.991.942.242.222.202.182.162.142.132.112.102.092.082.072.062.062.052.001.951.901.852.182.152.132.112.092.082.062.052.042.022.012