One-Tailed Test

Definition

A one-tailed test is a statistical hypothesis test in which the critical region is located in only one tail of the probability distribution. This type of test is used when the researcher is interested in determining if the population parameter is either greater than or less than a specified value, but not both.

5 Must Know Facts For Your Next Test

1. In a one-tailed test, the null hypothesis (H0) and the alternative hypothesis (Ha) are formulated to specify the direction of the effect.
2. The critical region in a one-tailed test is located in either the upper or lower tail of the probability distribution, depending on the alternative hypothesis.
3. One-tailed tests have greater statistical power than two-tailed tests when the alternative hypothesis specifies the direction of the effect correctly.
4. The choice between a one-tailed or two-tailed test should be based on the research question and the prior expectations about the direction of the effect.
5. One-tailed tests are commonly used in hypothesis testing for two means and two proportions (topic 10.5) as well as in tests of two variances (topic 13.4).

Review Questions

• Explain the key differences between a one-tailed and a two-tailed hypothesis test.
  • The primary difference between a one-tailed and a two-tailed hypothesis test lies in the location of the critical region. In a one-tailed test, the critical region is located in only one tail of the probability distribution, whereas in a two-tailed test, the critical region is located in both tails. This means that a one-tailed test is used when the researcher is interested in determining if the population parameter is either greater than or less than a specified value, but not both. In contrast, a two-tailed test is used when the researcher is interested in detecting a difference in either direction.
• Describe how the choice between a one-tailed or two-tailed test can impact the statistical power of the hypothesis test.
  • The choice between a one-tailed or two-tailed test can have a significant impact on the statistical power of the hypothesis test. One-tailed tests generally have greater statistical power than two-tailed tests when the alternative hypothesis specifies the direction of the effect correctly. This is because the critical region in a one-tailed test is located in only one tail of the probability distribution, resulting in a larger critical value and a higher probability of rejecting the null hypothesis when it is false. Conversely, two-tailed tests are more appropriate when the researcher does not have a strong a priori expectation about the direction of the effect, as they can detect differences in either direction.
• Explain how the one-tailed test is used in the context of hypothesis testing for two means and two proportions (topic 10.5) as well as in tests of two variances (topic 13.4).
  • The one-tailed test is commonly used in the context of hypothesis testing for two means and two proportions (topic 10.5) when the researcher is interested in determining if the population mean or proportion of one group is either greater than or less than the population mean or proportion of another group. Similarly, in tests of two variances (topic 13.4), the one-tailed test can be used to determine if the population variance of one group is either greater than or less than the population variance of another group. The choice between a one-tailed or two-tailed test in these contexts should be based on the research question and the prior expectations about the direction of the effect.

Related terms

Hypothesis Testing: The process of using statistical analysis to determine whether a hypothesis about a parameter of a population is likely to be true or false.

Two-Tailed Test: A statistical hypothesis test in which the critical region is located in both tails of the probability distribution, allowing for the detection of a difference in either direction.

p-value: The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.