One-sided hypothesis test

A one-sided test targets deviations in one specified direction, such as $\theta >{\theta }_0$. If larger values of a statistic $T$ indicate this direction, its p-value is an upper-tail null probability $P_0(T\ge t_{\mathrm{obs}})$. The direction should be chosen from the scientific question before examining the data. An upper normal test uses $1-\Phi (z)$; a lower test uses $\Phi (z)$.