Google

A one-tailed test has a less extreme critical value than a two-tailed test, providing a better chance of rejecting the null hypothesis if the observed difference aligns with the predicted direction. However, if the sample mean differs in the unexpected direction, a one-tailed test offers zero chance of rejecting the null hypothesis, unlike a two-tailed test which can detect effects in either direction.

Comparing One-Tailed and Two-Tailed $$t$$-Tests

Using a one-tailed test instead of a two-tailed test changes the critical value and the ease of rejecting the null hypothesis. For example, if a researcher has a strong theoretical reason to expect an underestimation, a one-tailed test will have a less extreme critical value (e.g., $$-1.833$$) compared to a two-tailed test (e.g., $$\pm 2.262$$) for the same degrees of freedom. This makes it easier to reject the null hypothesis in the predicted direction. However, if the actual results are in the opposite direction (e.g., an overestimation instead of underestimation), the researcher cannot reject the null hypothesis, regardless of how extreme the difference is.

Example of Changing from a Two-Tailed to a One-Tailed $$t$$-Test

A one-tailed t-test has a less extreme critical value than a two-tailed t-test, making it easier to reject the null hypothesis when the observed difference is in the predicted direction.

Learn Before

Related