Bartlett-corrected likelihood-ratio statistic ($W_B=W/(1+b/n)$)

If ${\mathbb{E}}_{0}W=d(1+b/n+O(n^{-2}))$, the Bartlett-corrected statistic has mean $d+O(n^{-2})$. It is commonly calibrated against a chi-squared distribution with $d$ degrees of freedom. Equivalently, to the displayed order, one may multiply $W$ by $1-b/n$.