*5.1. Probability Distribution*

Analyzing the probability distribution, once the above treatment is worked out, becomes essential. In particular, probabilities *p* that the observed *χ* 2 exceeds by chance a value *<sup>χ</sup>*<sup>b</sup> for the correct model is clearly calculable and, in fact, *<sup>Q</sup>* provides a measure of the goodness of fit, as one infers it at the minimum of *χ* 2 . Two limiting cases, unfortunately, are possible, *Q* is too small or too large. The first occurrence leads to the fact that the model is either wrong or errors are underestimated and/or they do not distribute Gaussian. The second occurrence happens when either errors are overestimated or data are correlated while rarely it could also happen that the distribution is non-Gaussian.

In general, the statistical procedure suggests that *χ* 2 is roughly comparable with the data number. Consequently, using the reduced chi square, as the ratio between the chi square and the number of degrees of freedom, could be a useful trick to handle experimental workarounds.
