twotailed

Two-tailed, or twotailed, refers to a type of statistical hypothesis test in which the alternative hypothesis permits deviations in either direction from the null hypothesis. It is used when any difference from the null value would be important to detect.

In a two-tailed test, the null hypothesis typically states there is no effect or no difference (for example, μ = μ0). The alternative states that μ ≠ μ0. The test statistic, such as a z or t value, is assessed against critical values on both ends of the distribution, and the p-value represents the probability of observing a result as extreme as, or more extreme than, the one observed, in either direction.

Critical values are set so that the overall significance level α is split between the two tails (α/2 in each tail). For example, with α = 0.05, the rejection region lies in both tails beyond ±1.96 for a standard normal distribution, or the corresponding t-values for the sample size.

Two-tailed tests relate to two-sided confidence intervals: a 100(1−α)% confidence interval corresponds to a two-tailed test at level α, excluding parameter values outside the central region.

Advantages of the two-tailed approach include the ability to detect effects in either direction and its general applicability when no directional hypothesis is justified. Disadvantages include reduced power to detect a directional effect compared with a one-tailed test at the same α.

Commonly used with z-tests, t-tests, and other standard procedures, the two-tailed test remains a foundational concept in statistical hypothesis testing.