Testing uniform distribution
Test adaptation (that is, the goodness of fit) in general, has the purpose of verifying whether a variable under examination does or does not have a certain hypothesized distribution on the basis, as usual, of experimental data. It is used to compare a set of frequencies observed in a sample, with similar theoretical quantities assumed for the population. By means of the test, it is possible to quantitatively measure the degree of deviation between the two sets of values.
The results obtained in the samples do not always exactly agree with the theoretical results that are expected according to the rules of probability. Indeed, it is very rare for this to occur. For example, although theoretical considerations lead us to expect 100 heads and 100 tails from 200 flips of a coin, it is rare that these results are obtained exactly. However, despite this, we must not unnecessarily deduce that the coin is rigged.
The chi-squared test
The chi-squared test...