## F - Distribution Tables

The F distributions are a family of distributions with two parameters, the degrees of freedom of the sample variances in the numerator and denominator of the F statistic. The numerator degrees of freedom are always given first. The F distributions are not symmetric but are right skewed. The density curve figure illustrates the shape. Because sample variances cannot be negative, the F statistic takes only positive values and the F distribution has no probability below zero.The peak of the F density curve is near one; values far from one in either direction provide evidence against the hypothesis of equal standard deviations.

### Table of the Upper Percentage Points of the F distribution

 1 2 3 4 5 6 7 8 9 10 11 12 15 1 .05.01 1614052 2004999 2165403 2255625 2305764 2345859 2375928 2395981 2416022 2426056 2436082 2446106 2466157 2 .05.01 18.5198.49 19.0099.01 19.1699.17 19.2599.25 19.3999.30 19.3399.33 19.3699.34 19.3799.36 19.3899.38 19.3999.40 19.499.4 19.499.4 19.499.4 3 .05.01 10.1334.12 9.5530.81 9.2829.46 9.1228.71 9.0128.24 8.9427.91 8.8827.67 8.8427.49 8.8127.34 8.7827.23 8.7627.13 8.7427.05 8.7026.87 4 .05.01 7.7121.20 6.9418.00 6.5916.69 6.3915.98 6.2615.52 6.1615.21 6.0914.98 6.0414.80 6.0014.66 5.9614.54 5.9314.95 5.9114.37 5.8614.2 5 .05.01 6.6116.26 5.7913.27 5.4112.06 5.1911.39 5.0510.97 4.9510.67 4.8810.45 4.8210.27 4.7810.15 4.7410.05 4.709.96 4.689.89 4.629.72 6 .05.01 5.9913.74 5.1410.92 4.769.78 4.539.15 4.398.75 4.288.47 4.218.26 4.158.10 4.107.98 4.067.87 4.037.79 4.007.72 3.947.56 7 .05.01 5.5912.25 4.749.55 4.358.45 4.127.85 3.977.46 3.877.19 3.797.00 3.736.84 3.686.71 3.636.62 3.606.54 3.576.47 3.516.31 8 .05.01 5.3211.26 4.468.65 4.077.59 3.847.01 3.696.63 3.586.37 3.506.19 3.446.03 3.395.91 3.345.82 3.315.74 3.285.67 3.225.52 9 .05.01 5.1210.56 4.268.02 3.866.99 3.636.42 3.486.06 3.375.80 3.295.61 3.235.47 3.185.35 3.145.26 3.105.18 3.075.11 3.014.96 10 .05.01 4.9610.04 4.107.56 3.716.55 3.485.99 3.335.64 3.225.39 3.145.21 3.075.06 3.024.95 2.974.85 2.944.78 2.914.71 2.854.56 20 .05.01 4.307.95 3.445.72 3.054.82 2.824.31 2.663.99 2.553.76 2.463.59 2.403.45 2.343.35 2.303.26 2.313.30 2.283.23 2.203.09 30 .05.01 4.177.56 3.325.39 2.924.51 2.694.02 2.533.70 2.423.47 2.333.30 2.273.17 2.213.07 2.162.98 2.122.90 2.092.84 2.012.70 40 .05.01 4.087.31 3.235.18 2.844.31 2.613.83 2.453.51 2.343.29 2.253.12 2.182.99 2.122.89 2.082.80 2.042.73 2.002.66 1.922.52 50 .05.01 4.037.17 3.185.06 2.794.20 2.563.72 2.403.41 2.293.19 2.203.02 2.132.89 2.072.78 2.032.70 1.982.62 1.952.56 1.872.42 60 .05.01 4.007.08 3.154.98 2.764.13 2.533.65 2.373.34 2.253.12 2.172.95 2.102.82 2.042.72 1.992.63 1.952.56 1.922.50 1.842.35 70 .05.01 3.987.01 3.134.92 2.744.08 2.503.60 2.353.29 2.233.07 2.142.91 2.072.77 2.012.67 1.972.59 1.932.51 1.892.45 1.822.32 80 .05.01 3.966.96 3.114.88 2.724.04 2.483.56 2.333.25 2.213.04 2.122.87 2.052.74 1.992.64 1.952.55 1.912.48 1.882.41 1.802.28 100 .05.01 3.946.90 3.094.82 2.703.98 2.463.51 2.313.21 2.192.99 2.102.82 2.032.69 1.972.59 1.932.50 1.882.43 1.852.36 1.772.22 200 .05.01 3.896.76 3.044.71 2.653.88 2.423.41 2.263.11 2.142.89 2.062.73 1.982.60 1.932.50 1.882.41 1.832.34 1.802.28 1.722.13 400 .05.01 3.866.70 3.024.66 2.623.83 2.393.36 2.233.06 2.122.85 2.032.69 1.962.55 1.902.46 1.852.37 1.812.29 1.782.23 1.702.08 1000 .05.01 3.856.66 3.004.63 2.613.80 2.383.34 2.223.04 2.112.82 2.022.66 1.952.53 1.892.43 1.842.34 1.802.26 1.762.20 1.682.06 Inf .05.01 3.856.64 2.994.60 2.603.78 2.373.32 2.213.02 2.092.80 2.012.64 1.942.51 1.882.41 1.832.32 1.792.24 1.752.18 1.662.03