T is used to infer the association between the SNP and multivariate phenotypic traits. When the marginal p-values are independent, the statistic T follows a chi-squared distribution with 2m degrees of freedom so the p-value of T can be obtained straightforwardly. In reality, however, the phenotypic traits are always correlated so the chi-squared distribution with 2m degrees of freedom tends to underestimate the variance of the T statistic. The resulting chi-squared test is, therefore, too liberal.
