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A two-tailed test is an approach to hypothesis testing where researchers reject the null hypothesis if their calculated test statistic falls into the extreme regions of either the positive or negative tail of the distribution. This method utilizes two distinct critical values—an upper bound and a lower bound—and is appropriately chosen when researchers expect the sample mean to differ from the hypothetical population mean, but lack strong theoretical justification to predict whether it will be higher or lower.

Two-Tailed Test

A one-tailed test is a hypothesis test in which the null hypothesis is rejected only if the test statistic is extreme in one specific direction, which must be hypothesized prior to data collection. By utilizing only a single critical value, this test increases the likelihood of finding a statistically significant result if the data trends in the expected direction, but completely eliminates the possibility of rejecting the null hypothesis if the results go in the opposite direction.

One-Tailed Test

To illustrate a two-tailed test, consider a scenario with $$24$$ degrees of freedom where the critical values for an alpha level of $$.05$$ are $$2.064$$ and $$-2.064$$ (represented by red vertical lines in the accompanying distribution). Any computed $$t$$ score falling below $$-2.064$$ (the lowest $$2.5\%$$ of the distribution) or above $$2.064$$ (the highest $$2.5\%$$ of the distribution) is considered extreme. If a sample's $$t$$ score falls into either of these outer regions, the resulting $$p$$-value is less than $$.05$$, providing sufficient statistical evidence for the researcher to reject the null hypothesis.

Example of a Two-Tailed Test

An approach to hypothesis testing where researchers reject the null hypothesis if their calculated test statistic falls into the extreme regions of either the positive or negative tail of the distribution is called a ____ test.

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