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性质定义假设总体，与为来自X的两个独立样本，设统计量那么称统计量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假设总体与总体独立，为来自X的一个样本，为来自Y的一个样本，那么统计量那么称统计量F服从自由度

2、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，那么。性质3：设，那么。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：假设总体与独立，为来自X的一个样本，为来自Y的一个样本，为参数。那么统计量性质6：假设总体与独立，为来自X的一个样本，为来自Y的一个样本，那么统计量F统计学附录表F分布临界值表0.0050.10=0.005Fk1k21234568 1224123456789101112131415161718192021222324252627282930406012016211198.555.5531.3322.7818.6316.241

3、4.6913.6112.8312.2311.7511.3711.0610.8010.5810.3810.2210.079.949.839.739.639.559.489.419.349.289.239.188.838.498.1820000199.049.8026.2818.3114.4512.4011.0410.119.438.918.518.197.927.707.517.357.217.096.996.896.816.736.666.606.546.496.446.406.356.075.795.5421615199.247.4724.2616.5312.9210.889.608.728

4、.087.607.236.936.686.486.306.166.035.925.825.735.655.585.525.465.415.365.325.285.244.984.734.5022500199.246.1923.1515.5612.0310.058.817.967.346.886.526.236.005.805.645.505.375.275.175.095.024.954.894.844.794.744.704.664.624.374.143.9223056199.345.3922.4614.9411.469.528.307.476.876.426.075.795.565.37

5、5.215.074.964.854.764.684.614.544.494.434.384.344.304.264.233.993.763.5523437199.344.8421.9714.5111.079.167.957.136.546.105.765.485.265.074.914.784.664.564.474.394.324.264.204.154.104.064.023.983.953.713.493.2823925199.444.1321.3513.9610.578.687.506.696.125.685.355.084.864.674.524.394.284.184.094.01

6、3.943.883.833.783.733.693.653.613.583.353.132.9324426199.443.3920.7013.3810.038.187.016.235.665.244.914.644.434.254.103.973.863.763.683.603.543.473.423.373.333.283.253.213.182.952.742.5424940199.542.6220.0312.789.477.656.505.735.174.764.434.173.963.793.643.513.403.313.223.153.083.022.972.922.872.832

7、.792.762.732.502.292.0925465199.541.8319.3212.148.887.085.955.194.644.233.903.653.443.263.112.982.872.782.692.612.552.482.432.382.332.292.252.212.181.931.691.43=0.01 Fk1k2 123456812241234567891011121314151617181920212223242526272829304060120405298.4934.1221.2016.2613.7412.2511.2610.5610.049.659.339.

8、078.868.688.538.408.288.188.108.027.947.887.827.777.727.687.647.607.567.317.086.856.64499999.0130.8118.0013.2710.929.558.658.027.567.206.936.706.516.366.236.116.015.935.855.785.725.665.615.575.535.495.455.425.395.184.984.794.60540399.1729.4616.6912.069.788.457.596.996.556.225.955.745.565.425.295.185

9、.095.014.944.874.824.764.724.684.644.604.574.544.514.314.133.953.78562599.2528.7115.9811.399.157.857.016.425.995.675.415.205.034.894.774.674.584.504.434.374.314.264.224.184.144.114.074.044.023.833.653.483.32576499.3028.2415.5210.978.757.466.636.065.645.325.064.864.694.564.444.344.254.174.104.043.993

10、.943.903.863.823.783.753.733.703.513.343.173.02585999.3327.9115.2110.678.477.196.375.805.395.074.824.624.464.324.204.104.013.943.873.813.763.713.673.633.593.563.533.503.473.293.122.962.80598199.3627.4914.8010.298.106.846.035.475.064.744.504.304.144.003.893.793.713.633.563.513.453.413.363.323.293.263.233.203.172.992.822.662.51610699.4227.0514.379.897.726.475.675.114.714.404.163.963.803.673.553.453.373.303.233.173.123.073.032.992.962.932.902.872.842.662.502.342.186234