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Section B.3 Chi-Squared Distribution

Figure B.3.1. \(\chi^2\) Distribution Probabilities
\(df\) \(\chi^2_{0.99}\) \(\chi^2_{0.95}\) \(\chi^2_{0.90}\) \(\chi^2_{0.10}\) \(\chi^2_{0.05}\) \(\chi^2_{0.01}\)
\(1\) 0.000 0.004 0.016 2.706 3.841 6.635
\(2\) 0.000 0.103 0.211 4.605 5.991 9.210
\(3\) 0.115 0.352 0.584 6.251 7.815 11.345
\(4\) 0.297 0.711 1.064 7.779 9.488 13.277
\(5\) 0.554 1.145 1.610 9.236 11.070 15.086
\(6\) 0.872 1.635 2.204 10.645 12.592 16.812
\(7\) 1.239 2.167 2.833 12.017 14.067 18.475
\(8\) 1.646 2.733 3.490 13.362 15.507 20.090
\(9\) 2.088 3.325 4.168 14.684 16.919 21.666
\(10\) 2.558 3.940 4.865 15.987 18.307 23.209
\(11\) 3.053 4.575 5.578 17.275 19.675 24.725
\(12\) 3.571 5.226 6.304 18.549 21.026 26.217
\(13\) 4.107 5.892 7.042 19.812 22.362 27.688
\(14\) 4.660 6.571 7.790 21.064 23.685 29.141
\(15\) 5.229 7.261 8.547 22.307 24.996 30.578
\(16\) 5.812 7.962 9.312 23.542 26.296 32.000
\(17\) 6.408 8.672 10.085 24.769 27.587 33.409
\(18\) 7.015 9.390 10.865 25.989 28.869 34.805
\(19\) 7.633 10.117 11.651 27.204 30.144 36.191
\(20\) 8.260 10.851 12.443 28.412 31.410 37.566
\(25\) 11.524 14.611 16.473 34.382 37.652 44.314
\(30\) 14.953 18.493 20.599 40.256 43.773 50.892
\(35\) 18.509 22.465 24.797 46.059 49.802 57.342
\(40\) 22.164 26.509 29.051 51.805 55.758 63.691
\(45\) 25.901 30.612 33.350 57.505 61.656 69.957
\(50\) 29.707 34.764 37.689 63.167 67.505 76.154
\(60\) 37.485 43.188 46.459 74.397 79.082 88.379
\(70\) 45.442 51.739 55.329 85.527 90.531 100.425
\(80\) 53.540 60.391 64.278 96.578 101.879 112.329
\(90\) 61.754 69.126 73.291 107.565 113.145 124.116
\(100\) 70.065 77.929 82.358 118.498 124.342 135.807
Table B.3.2. \(\chi^2\) Distribution Probabilities