= Continuity correction
{title2=$t\mapsto t-\tfrac12\text{ for an upper tail}$}
{wiki}
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 $1-\Phi((t-\tfrac12-E(T))/\sqrt{\operatorname{Var}(T)})$. Lower tails use the boundary $t+\tfrac12$. The correction is used in approximate <Wilcoxon signed-rank tests> and <Wilcoxon rank sum tests>; tied ranks also require the appropriate variance adjustment.
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