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.

When a psychology researcher predicts that a treatment will have an effect in a specific direction, what is the primary trade-off of choosing a one-tailed $t$-test instead of a two-tailed $t$-test?

A psychology researcher is analyzing data from a study on a new therapy. Match each research situation with the corresponding consequence of choosing either a one-tailed or two-tailed $t$-test.

A psychology researcher predicts that a new mindfulness exercise will reduce symptoms of social anxiety. Arrange the following $t$-test scenarios in order from the one with the greatest statistical power (easiest to reject the null hypothesis) to the one with the lowest statistical power (impossible to reject), assuming the sample results show a reduction in anxiety unless otherwise specified.

If a researcher conducts a one-tailed $t$-test and the sample mean differs in the unexpected direction, what is the chance of rejecting the null hypothesis?

If a researcher predicts a specific direction for their results, choosing a one-tailed $t$-test over a two-tailed $t$-test guarantees a higher chance of rejecting the null hypothesis, regardless of the direction of the observed sample mean.

A researcher is evaluating the trade-offs of using a one-tailed $t$-test to study a new therapy's effectiveness. Although this choice provides a better chance of rejecting the null hypothesis if the therapy works as predicted, the researcher must recognize that if the therapy unexpectedly makes symptoms significantly worse, their test choice provides a(n) _____ chance of rejecting the null hypothesis.

A researcher is selecting between a one-tailed and two-tailed $t$-test for an upcoming study. Match each research situation to the correct test characteristic or outcome.

A researcher analyzing the asymmetry of one-tailed versus two-tailed $t$-tests concludes that when the sample mean differs from the hypothetical population mean in the direction opposite to the researcher's prediction, a one-tailed $t$-test yields a _____ probability of rejecting the null hypothesis, even if the observed difference is very large.

A researcher is deciding whether to switch from a two-tailed to a one-tailed $t$-test for a study. Arrange the following evaluative steps in the correct logical order for making a methodologically defensible decision.

Based on the provided comparisons, explain the difference in critical values between one-tailed and two-tailed $t$-tests, and recall the consequences of these differences when a sample mean deviates in the predicted versus the unexpected direction.

Using the principles of comparing one-tailed and two-tailed tests, explain why the researcher cannot reject the null hypothesis in this situation, and discuss how the outcome would differ if she had initially chosen a two-tailed $t$-test.

A clinical researcher expects that a new therapeutic drug will decrease symptom severity and selects a one-tailed $t$-test to analyze the data. Apply the concepts of critical values and directional outcomes to explain the risk the researcher takes if the drug actually increases symptom severity.