Two-sided hypothesis test

A two-sided test detects departures in either direction from the null hypothesis, for example $\theta \ne {\theta }_0$. With a continuous symmetric null statistic centred at zero, its p-value is $P_0(|T|\ge |t_{\mathrm{obs}}|)=2P_0(T\ge |t_{\mathrm{obs}}|)$. This is the usual coefficient test printed by Gaussian regression summaries, unlike a directional one-sided comparison.