Sigma | 1σ | 1.28 | 1.64 | 1.96 | 2σ | 2.58 | 3σ | 3.29 | 4σ |

CI % | 68.3% | 80% | 90% | 95% | 95.45% | 99% | 99.73% | 99.9% | 99.99% |

P-value | 0.317 | 0.20 | 0.10 | 0.05 | 0.0455 | 0.01 | 0.0027 | 0.001 | 0.00006 |

chi2(k=1) | 1.00 | 1.64 | 2.71 | 3.84 | 4.00 | 6.63 | 9.00 | 10.83 | 16.00 |

chi2(k=2) | 2.30 | 3.22 | 4.61 | 5.99 | 6.18 | 9.21 | 11.83 | 13.82 | 19.33 |

chi2(k=3) | 3.53 | 4.64 | 6.25 | 7.81 | 8.02 | 11.34 | 14.16 | 16.27 | 22.06 |

chi2(k=4) | 4.72 | 5.99 | 7.78 | 9.49 | 9.72 | 13.28 | 16.25 | 18.47 | 24.50 |

chi2(k=5) | 5.89 | 7.29 | 9.24 | 11.07 | 11.31 | 15.09 | 18.21 | 20.52 | 26.77 |

chi2(k=6) | 7.04 | 8.56 | 10.64 | 12.59 | 12.85 | 16.81 | 20.06 | 22.46 | 28.91 |

chi2(k=7) | 8.18 | 9.80 | 12.02 | 14.07 | 14.34 | 18.48 | 21.85 | 24.32 | 30.96 |

chi2(k=8) | 9.30 | 11.03 | 13.36 | 15.51 | 15.79 | 20.09 | 23.57 | 26.12 | 32.93 |

chi2(k=9) | 10.42 | 12.24 | 14.68 | 16.92 | 17.21 | 21.67 | 25.26 | 27.88 | 34.85 |

chi2(k=10) | 11.54 | 13.44 | 15.99 | 18.31 | 18.61 | 23.21 | 26.90 | 29.59 | 36.72 |

The Python script used to generate this table is below. It uses the percentage point function (ppf) and cumulative distribution functions (cdf) from the scipy.stats.chi2 distribution in the SciPy stats library:

```
#!/usr/bin/python
import scipy.stats
import math
#stand deviations to calculate
sigma
```**=** [ 1.0,
math.sqrt(scipy.stats.chi2.ppf(0.8,1)),
math.sqrt(scipy.stats.chi2.ppf(0.9,1)),
math.sqrt(scipy.stats.chi2.ppf(0.95,1)),
2.0,
math.sqrt(scipy.stats.chi2.ppf(0.99,1)),
3.0,
math.sqrt(scipy.stats.chi2.ppf(0.999,1)),
4.0 ]
#confidence intervals these sigmas represent:
conf_int **=** [ scipy.stats.chi2.cdf( s******2,1) **for** s **in** sigma ]
#degrees of freedom to calculate
dof **=** range(1,11)
print "sigma \t" **+** "\t".join(["%1.2f"**%**(s) **for** s **in** sigma])
print "conf_int \t" **+** "\t".join(["%1.2f%%"**%**(100*****ci) **for** ci **in** conf_int])
print "p-value \t" **+** "\t".join(["%1.5f"**%**(1**-**ci) **for** ci **in** conf_int])
**for** d **in** dof:
chi_squared **=** [ scipy.stats.chi2.ppf( ci, d) **for** ci **in** conf_int ]
print "chi2(k=%d)\t"**%**d **+** "\t".join(["%1.2f" **%** c **for** c **in** chi_squared])