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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

When a researcher switches from a two-tailed t-test to a one-tailed t-test (with the same degrees of freedom and significance level), the critical value for the one-tailed test is less extreme than that of the two-tailed test, making it easier to reject the null hypothesis in the predicted direction.

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