The phi coefficient has been developed long ago. It is mainly used in the case of 2×2 contingency tables involving two variables that are dichotomous in nature. It can measure the association of the two dichotomous variables. In this thesis, we extend the traditional phi coefficient that formed by two variables to arbitrary k variables, and show that k*(k-1)/2 phi coefficients are asymptotically normal. Moreover, we derive confidence regions and two-sided test of mul-tivariate phi coefficients, simulate critical values with smaller sample size, and discuss the powers of tests.