Chi-Square Distributions Table: Probability and Degrees of Freedom, Slides of Applied Statistics

A chi-square distributions table showing the cumulative probabilities and right tail probabilities for various degrees of freedom (df). The table can be used to determine the probability of observing a certain chi-square value or the chi-square value corresponding to a given probability level. This information is essential in statistical hypothesis testing and goodness-of-fit tests.

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TABLE C: Chi-Square distributions
cum probability 0.025 0.80 0.90 0.95 0.975 0.99 0.995 0.999 0.9995
right tail 0.975 0.2 0.1 0.05 0.025 0.01 0.005 0.001 0.0005
df
10.00098 1.64 2.71 3.84 5.02 6.63 7.88 10.83 12.12
20.051 3.22 4.61 5.99 7.38 9.21 10.60 13.82 15.20
30.216 4.64 6.25 7.81 9.35 11.34 12.84 16.27 17.73
40.48 5.99 7.78 9.49 11.14 13.28 14.86 18.47 20.00
50.83 7.29 9.24 11.07 12.83 15.09 16.75 20.51 22.11
61.24 8.56 10.64 12.59 14.45 16.81 18.55 22.46 24.10
71.69 9.80 12.02 14.07 16.01 18.48 20.28 24.32 26.02
82.18 11.03 13.36 15.51 17.53 20.09 21.95 26.12 27.87
92.70 12.24 14.68 16.92 19.02 21.67 23.59 27.88 29.67
10 3.25 13.44 15.99 18.31 20.48 23.21 25.19 29.59 31.42
11 3.82 14.63 17.28 19.68 21.92 24.73 26.76 31.26 33.14
12 4.40 15.81 18.55 21.03 23.34 26.22 28.30 32.91 34.82
13 5.01 16.98 19.81 22.36 24.74 27.69 29.82 34.53 36.48
14 5.63 18.15 21.06 23.68 26.12 29.14 31.32 36.12 38.11
15 6.26 19.31 22.31 25.00 27.49 30.58 32.80 37.70 39.72
16 6.91 20.47 23.54 26.30 28.85 32.00 34.27 39.25 41.31
17 7.56 21.61 24.77 27.59 30.19 33.41 35.72 40.79 42.88
18 8.23 22.76 25.99 28.87 31.53 34.81 37.16 42.31 44.43
19 8.91 23.90 27.20 30.14 32.85 36.19 38.58 43.82 45.97
20 9.59 25.04 28.41 31.41 34.17 37.57 40.00 45.31 47.50
21 10.28 26.17 29.62 32.67 35.48 38.93 41.40 46.80 49.01
22 10.98 27.30 30.81 33.92 36.78 40.29 42.80 48.27 50.51
23 11.69 28.43 32.01 35.17 38.08 41.64 44.18 49.73 52.00
24 12.40 29.55 33.20 36.42 39.36 42.98 45.56 51.18 53.48
25 13.12 30.68 34.38 37.65 40.65 44.31 46.93 52.62 54.95
30 16.79 36.25 40.26 43.77 46.98 50.89 53.67 59.70 62.16
40 24.43 47.27 51.81 55.76 59.34 63.69 66.77 73.40 76.10
50 32.36 58.16 63.17 67.50 71.42 76.15 79.49 86.66 89.56
60 40.48 68.97 74.40 79.08 83.30 88.38 91.95 99.61 102.7
80 57.15 90.41 96.58 101.9 106.6 112.3 116.3 124.8 128.3
100 74.22 111.7 118.5 124.3 129.6 135.8 140.2 149.4 153.2
chisq-table.xls 7/11/2005

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  • TABLE C: Chi-Square distributions cum probability right tail df 12 0.00098 0.0250.975 0.051 0.80 1.643.22 0.2 0.90 2.714.61 0.1 0.950.05 3.845.99 0.9750.025 5.027.38 0.990.01 6.639.21 0.9950.005 10.607.88 0.9990.001 10.8313.82 0.99950.0005 12.1215. - 345678 0.2160.480.831.241.692.18 11.034.645.997.298.569.80 10.6412.0213.366.257.789.24 11.0712.5914.0715.517.819.49 11.1412.8314.4516.0117.539.35 11.3413.2815.0916.8118.4820.09 12.8414.8616.7518.5520.2821.95 16.2718.4720.5122.4624.3226.12 17.7320.0022.1124.1026.0227. - 10111213149 2.703.253.824.405.015.63 12.2413.4414.6315.8116.9818.15 14.6815.9917.2818.5519.8121.06 16.9218.3119.6821.0322.3623.68 19.0220.4821.9223.3424.7426.12 21.6723.2124.7326.2227.6929.14 23.5925.1926.7628.3029.8231.32 27.8829.5931.2632.9134.5336.12 29.6731.4233.1434.8236.4838. - 151617181920 6.266.917.568.238.919.59 19.3120.4721.6122.7623.9025.04 22.3123.5424.7725.9927.2028.41 25.0026.3027.5928.8730.1431.41 27.4928.8530.1931.5332.8534.17 30.5832.0033.4134.8136.1937.57 32.8034.2735.7237.1638.5840.00 37.7039.2540.7942.3143.8245.31 39.7241.3142.8844.4345.9747. - 212223242530 10.2810.9811.6912.4013.1216.79 26.1727.3028.4329.5530.6836.25 29.6230.8132.0133.2034.3840.26 32.6733.9235.1736.4237.6543.77 35.4836.7838.0839.3640.6546.98 38.9340.2941.6442.9844.3150.89 41.4042.8044.1845.5646.9353.67 46.8048.2749.7351.1852.6259.70 49.0150.5152.0053.4854.9562.
    • 10040506080 24.4332.3640.4857.1574.22 47.2758.1668.9790.41111.7 51.8163.1774.4096.58118.5 55.7667.5079.08101.9124.3 59.3471.4283.30106.6129.6 63.6976.1588.38112.3135.8 66.7779.4991.95116.3140.2 73.4086.6699.61124.8149.4 76.1089.56102.7128.3153.
  • chisq-table.xls 7/11/