2] has an independent noncentral chi-square distribution with v degrees of freedom and noncentrality parameter [lambda], then
Suppose S is a random variable independent of Z such that vS has a chi-square distribution with v degrees of freedom.
Schatzoff , Pillai and Gupta , Lee , and Davis  tabulate multiplying factors C to obtain upper percentage points of the distribution of the Wilks's Likelihood Ratio Test Statistic - [n - p - (1/2) (m - r + 1)] logW from the percentage points of the chi-square distribution for multivariate analysis of variance.
Leon Harter, More Tables of the Incomplete Gamma Function Ratio and of Percentage Points of the Chi-Square Distribution, U.
Leon Harter, A New Table of Percentage Points of the Chi-Square Distribution, Biometrika 51, 231-239 (1964).
2] statistic is then calculated from this combined table using Equation 5, and compared to a chi-square distribution with J-1 degrees of freedom.
Comparing this to a chi-square distribution with 1 degree of freedom gives a p-value of .
As above, this can be compared to a chi-square distribution with J-1 degrees of freedom.
2]/MAF has a chi-square distribution with J - 1 degrees of freedom, then [X.