Suggerimenti per l'impiego del test chi-quadrato

Considerations about the application of the chi-squared test One of the most frequent criticisms about the chi-squared test is its sensitivity. Some authors say that very slight differences from the null hypothesis, for large sample sizes, may lead to its rejection. The purpose of the present work, after introducing a distance D from the k probabilities of an alternative hypothesis and the null, is to determine the minimum sample sizes needed to simultaneously control the probability of the errors of first and second kind. It is shown that considerable sample sizes n are required, hence the criticisms on the sensibility of the test appear to be unsubstantiated. Furthermore, we show how the Pearson Chi-square statistics can be employed, jointly with the distance D, to obtain a test with balanced errors. This means a test which can be used under controlling, through a given ratio, the maximum value of the error of second kind and the error of first kind.