# Statistical Analysis for Physics Research Project

#### DTMsurf

##### New Member
Important concepts for Problem: Chi-Square test, p-value, Sigma Significance

I am an undergraduate Physics student working on a research project which involves a certain level of statistical analysis that I have some lacking knowledge about. I have built a macro that has the capability to output both Chi^2 and p-value test scores between two histograms, one filled by a simulation of neutrino event counts and the other filled by this same simulation while incorporating a theory of heavy neutrinos. My professor has now tasked me with converting my sensitivity scores into a form that I do not have an equation or method to obtain.

Goal: To convert the p-value or chi^2 score into a sensitivity score in terms of a constant multiplied by the standard deviation of a normal distribution called the “Sigma Significance”. An example of a score like this would be 1.57*(sigma) or 0.82*(sigma) in which a high amount would correspond to a lower p-value and higher chi^2 while a low sigma significance would correspond to a high p-value and low chi^2 score.

If any other information may be needed to solve this problem please let me know and I can try and provide it.

#### katxt

##### Well-Known Member
I haven't heard of this one. There is an Excel function =NORMSINV(...) which will give you a z value from a p value. p is the area to the left of z. This may be of use. One problem is that many test p values are two tailed and chi square is one tailed.
So, guessing what your professor wants ... p = 0.1 z =NORMSINV(0.1) = -1.28, score = 1.28*(sigma).
Who knows?

#### DTMsurf

##### New Member
Yeah from what I understand the analysis is 1 tailed, Sigma significance is something that everyone in my research group is struggling to figure out.