 Bartlett correction

A Bartlett correction rescales a regular likelihood-ratio test statistic so that its null expected value matches its limiting chi-squared degrees of freedom to a higher asymptotic order. If ${\mathbb{E}}_{0}W=d(1+b/n+O(n^{-2}))$, divide $W$ by $1+b/n$. The operation uses a model-specific Bartlett correction coefficient; matching the mean alone is not a general proof of any claimed distributional error rate.