# Statistical-tests

## Intro

In HERMES, like in any other experiment, it is important that the measured quantity (let's say an asymmetry) be tested for possible dependencies on quantities it should not depend on, and for randomness. Each test has its own goals, and specific cases in which it can be used, and in most cases more than one test should be used.

As an example, let's suppose that the asymmetry grows steadily in time, while always remaining within the limits of small fluctuations with respect to its uncertainties. In such a case a chi2 test would give a very good result, while other tests (as the Wilcoxon test) may highlight the fact that there is a trend in the data. A way to see it is to assign an A to the values smaller than the average and a B to the values larger than the average, and to see the time dependence of such a succession of A's and B's.

## Essentials

Tests of randomness can be applied to eg. time (or cut, or binning, eg. zvertex) dependences of asymmetries or cross-sections. The most commonly used tests are:

• t-test (student's test)
• z-test: effectively a chi2 test. It checks the spread of the asymmetry wrt the average value, to see if these can be attributed to randomness.
• Wilcoxon test
• Mann Whitney test: checks for trends on data. It requires data to be separated into two samples,with the possibility to ordering the elements of the set according to an ordering criterion. The purpose is to understand if there is a trend in the data, i.e. if one set is consistently above or below the other set. It can be used for example to see if over time, the top asymmetry was consistently above or below the bottom asymmetry.