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Percentage Points for the Chi-Squared Distribution


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If X has a χ2 distribution with ν degrees of freedom, then a tabulated value, x, is such that P(X < x)=p%.

p(%)

νLower tailUpper tail

0.52.55909597.59999.599.9

10.0439270.0398210.0239322.7063.8415.0246.6357.87910.83

20.010030.050640.10264.6055.9917.3789.21010.6013.82

30.071720.21580.35186.2517.8159.34811.3412.8416.27

40.20700.48440.71077.7799.48811.1413.2814.8618.47

50.41170.83121.1459.23611.0712.8315.0916.7520.52

60.67571.2371.63510.6412.5914.4516.8118.5522.46

70.98931.6902.16712.0214.0716.0118.4820.2824.32

81.3442.1802.73313.3615.5117.5320.0921.9526.12

91.7352.7003.32514.6816.9219.0221.6723.5927.88

102.1563.2473.94015.9918.3120.4823.2125.1929.59

112.6033.8164.57517.2819.6821.9224.7226.7631.26

123.0744.4045.22618.5521.0323.3426.2228.3032.91

133.5655.0095.89219.8122.3624.7427.6929.8234.53

144.0755.6296.57121.0623.6826.1229.1431.3236.12

154.6016.2627.26122.3125.0027.4930.5832.8037.70

165.1426.9087.96223.5426.3028.8532.0034.2739.25

175.6977.5648.67224.7727.5930.1933.4135.7240.79

186.2658.2319.39025.9928.8731.5334.8137.1642.31

196.8448.90710.1227.2030.1432.8536.1938.5843.82

207.4349.59110.8528.4131.4134.1737.5740.0045.31

218.03410.2811.5929.6232.6735.4838.9341.4046.80

228.64310.9812.3430.8133.9236.7840.2942.8048.27

239.26011.6913.0932.0135.1738.0841.6444.1849.73

249.88612.4013.8533.2036.4239.3642.9845.5651.18

2510.5213.1214.6134.3837.6540.6544.3146.9352.62

3013.7916.7918.4940.2643.7746.9850.8953.6759.70

4020.7124.4326.5151.8155.7659.3463.6966.7773.40

5027.9932.3634.7663.1767.5071.4276.1579.4986.66

6035.5340.4843.1974.4079.0883.3088.3891.9599.61

7043.2848.7651.7485.5390.5395.02100.4104.2112.3

8051.1757.1560.3996.58101.9106.6112.3116.3124.8

9059.2065.6569.13107.6113.1118.1124.1128.3137.2

10067.3374.2277.93118.5124.3129.6135.8140.2149.4

NB. For values of ν > 100 use the result that √2X has an approximate normal distribution with mean √2ν−1 and variance 1.

From A Dictionary of Statistics in Oxford Reference.

Subjects: Probability and Statistics.



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