## Feature #3990

### Add function to convert sigma for a given number of freedoms to TS value

Status: | New | Start date: | 02/17/2022 | |
---|---|---|---|---|

Priority: | Normal | Due date: | ||

Assigned To: | - | % Done: | 0% | |

Category: | - | |||

Target version: | - | |||

Duration: |

**Description**

The equation to use is at the bottom of

https://people.math.gatech.edu/~ecroot/3225/chisquare.pdf

In this equation *a* is the TS value that corresponds to a given significance level. Since *a* should be the outcome, the equation can only be solved iteratively.

To obtained the Probability on the left hand side of the equation, a Gaussian needs to be integrated over the interval `[-sigma,+sigma]`

, and the probability to be used is 1 - the integral.

The other parameters to use are `alpha = 1/2`

and *k* which is the number of degrees of freedom, see for example https://programmathically.com/chi-square-distribution-and-degrees-of-freedom/.

**Recurrence**

No recurrence.

### History

#### #1 Updated by Knödlseder Jürgen 11 months ago

**Target version**deleted ()*2.0.0*

#### #2 Updated by Knödlseder Jürgen 10 months ago

For 2 degrees of freedom the equation simplifies to

P(Chi2 > TS) = exp(-E/2.0)

hence

TS = -2 ln(P)

Sigma |
P |
TS |

1 | 1-0.6827 | 2.2958 |

2 | 1-0.9545 | 6.1801 |

3 | 1-0.9973 | 11.8290 |