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 almost 3 years ago
- Target version deleted (
2.0.0)
#2
Updated by Knödlseder Jürgen almost 3 years 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 |