  This paper is an extension of the work about the exponential increase of the
power of two non-parametric tests: the $ Z $-test and the chi-square
goodness-of-fit test. Subject to having auxiliary information, it is possible
to improve exponentially relative to the size of the sample the power of the
famous chi-square tests of independence and homogeneity. Improving the power of
these statistical tests by using auxiliary information makes it possible either
to reduce the probability of accepting the null hypothesis under the
alternative hypothesis, or to reduce the size of the sample necessary to reach
a predefined power. The suggested method is computational and some simple
statistical applications are presented to illustrate these results. The
framework of this work is non-parametric, so it can be applied to any kind of
data and any area using statistics.
