Normal approximation

A normal approximation replaces a sampling distribution by a normal distribution, often through a central limit theorem. In a Wald test, approximate statistical power is determined by the standardized difference under the alternative. This yields Neyman allocation for fixed treatment-specific variances.

A continuity correction shifts a discrete probability boundary by half a lattice spacing before using a continuous normal approximation. For an upper-tail event $T\ge t$ on a unit lattice, the approximation is $1-\Phi ((t-\frac{1}{2}-E(T))/\sqrt{\mathrm{Var}(T)})$. Lower tails use the boundary $t+\frac{1}{2}$. The correction is used in approximate Wilcoxon signed-rank tests and Wilcoxon rank sum tests; tied ranks also require the appropriate variance adjustment.