χ²分布具有可加性，也就是一个卡方加上另一个卡方，还是卡方，用公式表示就是：χ₁²+χ₂²=χ₃²。
因此χ₁²=χ₃²-χ₂²，也就是一个卡方减去一个卡方，还是卡方。
查χ²分布表时，按自由度及相应的概率去找到对应的值。
单侧概率：χ²单侧概率0.05(11)的查表方法就是，在第一列找到自由度11这一行，在第一行中找到概率0.05这一列，行列的交叉处为19.675。双侧概率：χ²双侧概率0.05(11)的查表方法就是，在第一列找到自由度11这一行，在第一行中找到概率0.05/2=0.025这一列，行列的交叉处为21.920 。
df0.9950.990.9750.950.900.100.050.0250.010.00510.000040.000160.0010.0040.0162.7063.8415.0246.6357.87920.0100.0200.0510.1030.2114.6055.9917.3789.21010.59730.0720.1150.2160.3520.5846.2517.8159.34811.34512.83840.2070.2970.4840.7111.0647.7799.48811.14313.27714.86050.4120.5540.8311.1451.6109.23611.07012.83315.08616.75060.6760.8721.2371.6352.20410.64512.59214.44916.81218.54870.9891.2391.6902.1672.83312.01714.06716.01318.47520.27881.3441.6462.1802.7333.49013.36215.50717.53520.09021.95591.7352.0882.7003.3254.16814.68416.91919.02321.66623.589102.1562.5583.2473.9404.86515.98718.30720.48323.20925.188112.6033.0533.8164.5755.57817.27519.67521.92024.72526.757123.0743.5714.4045.2266.30418.54921.02623.33726.21728.300133.5654.1075.0095.8927.04219.81222.36224.73627.68829.819144.0754.6605.6296.5717.79021.06423.68526.11929.14131.319154.6015.2296.2627.2618.54722.30724.99627.48830.57832.801165.1425.8126.9087.9629.31223.54226.29628.84532.00034.267175.6976.4087.5648.67210.08524.76927.58730.19133.40935.718186.2657.0158.2319.39010.86525.98928.86931.52634.80537.156196.8447.6338.90710.11711.65127.20430.14432.85236.19138.582207.4348.2609.59110.85112.44328.41231.41034.17037.56639.997218.0348.89710.28311.59113.24029.61532.67135.47938.93241.401228.6439.54210.98212.33814.04130.81333.92436.78140.28942.796239.26010.19611.68913.09114.84832.00735.17238.07641.63844.181249.88610.85612.40113.84815.65933.19636.41539.36442.98045.5592510.52011.52413.12014.61116.47334.38237.65240.64644.31446.9282611.16012.19813.84415.37917.29235.56338.88541.92345.64248.2902711.80812.87914.57316.15118.11436.74140.11343.19546.96349.6452812.46113.56515.30816.92818.93937.91641.33744.46148.27850.9932913.12114.25616.04717.70819.76839.08742.55745.72249.58852.3363013.78714.95316.79118.49320.59940.25643.77346.97950.89253.6724020.70722.16424.43326.50929.05151.80555.75859.34263.69166.7665027.99129.70732.35734.76437.68963.16767.50571.42076.15479.4906035.53437.48540.48243.18846.45974.39779.08283.29888.37991.9527043.27545.44248.75851.73955.32985.52790.53195.023100.425104.2158051.17253.54057.15360.39164.27896.578101.879106.629112.329116.3219059.19661.75465.64769.12673.291107.565113.145118.136124.116128.29910067.32870.06574.22277.92982.358118.498124.342129.561135.807140.169。