Section C.3 Chi-Square Probability Table
A chi-square probability table may be used to find tail areas of a chi-square distribution. When using a chi-square table, we examine a particular row for distributions with different degrees of freedom, and we identify a range for the area (e.g. 0.025 to 0.05). Note that the chi-square table provides upper tail values, which is different than the normal and \(t\)-distribution tables.
| Upper tail | 0.3 | 0.2 | 0.1 | 0.05 | 0.02 | 0.01 | 0.005 | 0.001 |
|---|---|---|---|---|---|---|---|---|
| df 1 | 1.07 | 1.64 | 2.71 | 3.84 | 5.41 | 6.63 | 7.88 | 10.83 |
| 2 | 2.41 | 3.22 | 4.61 | 5.99 | 7.82 | 9.21 | 10.60 | 13.82 |
| 3 | 3.66 | 4.64 | 6.25 | 7.81 | 9.84 | 11.34 | 12.84 | 16.27 |
| 4 | 4.88 | 5.99 | 7.78 | 9.49 | 11.67 | 13.28 | 14.86 | 18.47 |
| 5 | 6.06 | 7.29 | 9.24 | 11.07 | 13.39 | 15.09 | 16.75 | 20.52 |
| 6 | 7.23 | 8.56 | 10.64 | 12.59 | 15.03 | 16.81 | 18.55 | 22.46 |
| 7 | 8.38 | 9.80 | 12.02 | 14.07 | 16.62 | 18.48 | 20.28 | 24.32 |
| 8 | 9.52 | 11.03 | 13.36 | 15.51 | 18.17 | 20.09 | 21.95 | 26.12 |
| 9 | 10.66 | 12.24 | 14.68 | 16.92 | 19.68 | 21.67 | 23.59 | 27.88 |
| 10 | 11.78 | 13.44 | 15.99 | 18.31 | 21.16 | 23.21 | 25.19 | 29.59 |
| 15 | 17.32 | 19.31 | 22.31 | 25.00 | 28.26 | 30.58 | 32.80 | 37.70 |
| 20 | 22.77 | 25.04 | 28.41 | 31.41 | 35.02 | 37.57 | 39.99 | 45.31 |
| 25 | 28.17 | 30.68 | 34.38 | 37.65 | 41.57 | 44.31 | 46.93 | 52.62 |
| 30 | 33.53 | 36.25 | 40.26 | 43.77 | 47.96 | 50.89 | 53.67 | 59.70 |
| 40 | 44.16 | 47.27 | 51.81 | 55.76 | 60.44 | 63.69 | 66.77 | 73.40 |
| 50 | 54.72 | 58.16 | 63.17 | 67.50 | 72.61 | 76.15 | 79.49 | 86.66 |
| 60 | 65.23 | 68.97 | 74.40 | 79.08 | 84.58 | 88.38 | 91.95 | 99.61 |
| 80 | 86.12 | 90.41 | 96.58 | 101.88 | 108.07 | 112.33 | 116.32 | 124.84 |
| 100 | 106.91 | 111.67 | 118.50 | 124.34 | 131.14 | 135.81 | 140.17 | 149.45 |
