 Continuity correction

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.

Continuity correction is a statistical technique used when approximating the binomial distribution with a normal distribution. This is necessary because the binomial distribution is discrete, while the normal distribution is continuous. The correction helps improve the approximation by adjusting for the fact that the normal distribution can take on fractional values, while a binomial distribution only takes whole numbers. When using the normal approximation to the binomial distribution, the continuity correction involves adding or subtracting 0.5 to the discrete binomial variable.