  Introduction: there is an ongoing debate about directional inference of
two-sided hypothesis tests for which some authors argue that rejecting $\theta
= \theta_0$ does not allow to conclude that $\theta > \theta_0$ or $\theta <
\theta_0$ but only that $\theta \neq \theta_0$, while others argue that this is
a minor error without practical consequence.
  Discussion: new elements are brought to the debate. It is shown that the
directional interpretation of some non-directional hypothesis tests about
Receiver Operating Characteristic (ROC) and survival curves may lead to
inflated type III error rates with a probability of concluding that a
difference exists in the opposite side of the actual difference that can reach
50% in the worst case. Some of the issues of directional tests also apply to
two-sided confidence intervals (CIs). It is shown that equal-tailed CIs should
be preferred to shortest CIs. New assessment criteria of two-sided CIs and
hypothesis tests are proposed to provide a reliable directional interpretation:
partial left-sided and right-sided $\alpha$ error rates for hypothesis tests,
probabilities of overestimation and underestimation $\alpha_L$ and $\alpha_U$
and interval half-widths for two-sided CIs.
  Conclusion: two-sided CIs and two-sided tests are interpreted directionally.
This implies that directional interpretation be taken in account in the
development and evaluation of confidence intervals and tests.
