Two-sided test

A two-sided test has an alternative hypothesis using a not-equal sign, so a departure from the null in either direction counts as evidence.

Use a two-sided alternative when you want to detect any change rather than a change in a specific direction, which fits most research questions. Because both tails count, the p-value is twice the one-tail area whenever the null distribution is symmetric. For example, a test statistic of z=1.75z = 1.75 gives a p-value of 2×0.0401=0.08022 \times 0.0401 = 0.0802, against 0.0401 for the matching one-sided test. A two-sided test at α=0.05\alpha = 0.05 (alpha, the significance level) usually agrees with the 95% confidence interval, though for proportions the two can disagree in close cases because they use different standard errors.

Where this comes up

More hypothesis testing terms, or browse the full statistics glossary.