One-Tailed Test

Definition

A one-tailed test is a statistical hypothesis test in which the alternative hypothesis specifies the direction of the difference between the population parameter and the hypothesized value. It is used when the researcher is interested in determining whether the parameter is greater than or less than the hypothesized value, but not both.

5 Must Know Facts For Your Next Test

1. In a one-tailed test, the researcher is only interested in one direction of the difference between the population parameter and the hypothesized value, either greater than or less than.
2. The critical region for a one-tailed test is located in only one tail of the sampling distribution, either the upper tail or the lower tail, depending on the alternative hypothesis.
3. The test statistic for a one-tailed test is compared to a critical value that corresponds to the chosen significance level and the direction of the alternative hypothesis.
4. One-tailed tests have more statistical power than two-tailed tests when the alternative hypothesis specifies the direction of the difference.
5. One-tailed tests are commonly used in clinical trials, where the researcher is interested in determining if a new treatment is better than the standard treatment (one-tailed upper), or if a new treatment is worse than the standard treatment (one-tailed lower).

Review Questions

• Explain how a one-tailed test differs from a two-tailed test in the context of hypothesis testing.
  • The key difference between a one-tailed test and a two-tailed test is the alternative hypothesis. In a one-tailed test, the alternative hypothesis specifies the direction of the difference between the population parameter and the hypothesized value, either greater than or less than. In a two-tailed test, the alternative hypothesis only specifies that the population parameter is different from the hypothesized value, but does not specify the direction of the difference. This means that the critical region for a one-tailed test is located in only one tail of the sampling distribution, while the critical region for a two-tailed test is split between the two tails.
• Describe the scenarios in which a one-tailed test would be more appropriate than a two-tailed test.
  • A one-tailed test is more appropriate than a two-tailed test when the researcher is only interested in determining if the population parameter is greater than or less than the hypothesized value, but not both. This is common in situations where the researcher has a specific directional hypothesis, such as in clinical trials where the goal is to determine if a new treatment is better than the standard treatment. One-tailed tests have more statistical power than two-tailed tests when the alternative hypothesis specifies the direction of the difference, as the critical region is located in only one tail of the sampling distribution.
• Analyze the implications of choosing a one-tailed test over a two-tailed test in the context of hypothesis testing.
  • The choice between a one-tailed test and a two-tailed test can have significant implications for the interpretation of the results and the conclusions drawn from the hypothesis test. By choosing a one-tailed test, the researcher is essentially making a stronger claim about the directionality of the difference between the population parameter and the hypothesized value. This can lead to a higher probability of rejecting the null hypothesis, as the critical region is located in only one tail of the sampling distribution. However, this also means that the researcher is making a more specific and potentially riskier claim, as they are committing to a particular direction of the difference. In contrast, a two-tailed test is more conservative, as it does not make any assumptions about the direction of the difference, and the critical region is split between the two tails of the sampling distribution.

Related terms

Null Hypothesis: The null hypothesis is a statement that there is no significant difference between a population parameter and a hypothesized value.

Alternative Hypothesis: The alternative hypothesis is a statement that there is a significant difference between a population parameter and a hypothesized value.

Two-Tailed Test: A two-tailed test is a statistical hypothesis test in which the alternative hypothesis specifies that the population parameter is different from the hypothesized value, but does not specify the direction of the difference.