Two-Tailed Test

Definition

A two-tailed test is a statistical hypothesis test in which the critical region is split into two tails of the sampling distribution, one in each direction from the null hypothesis value. It is used to determine if a parameter is significantly different from a specified value, without specifying the direction of the difference.

5 Must Know Facts For Your Next Test

1. A two-tailed test is used when the alternative hypothesis does not specify the direction of the difference, only that there is a difference.
2. The critical region for a two-tailed test is split into two equal tails, one in each direction from the null hypothesis value.
3. The p-value for a two-tailed test is the probability of obtaining a test statistic at least as extreme as the one observed, in either direction.
4. Two-tailed tests are more conservative than one-tailed tests, as they require a larger test statistic to reject the null hypothesis.
5. Two-tailed tests are commonly used in hypothesis testing for comparing two independent population means, comparing two independent population proportions, and testing the significance of a correlation coefficient.

Review Questions

• Explain the difference between a two-tailed test and a one-tailed test in the context of hypothesis testing.
  • The key difference between a two-tailed test and a one-tailed test is the direction of the alternative hypothesis. In a two-tailed test, the alternative hypothesis does not specify the direction of the difference, only that there is a significant difference in either direction from the null hypothesis value. The critical region for a two-tailed test is split into two equal tails, one in each direction from the null hypothesis. In contrast, a one-tailed test has the critical region located entirely in one tail of the sampling distribution, either above or below the null hypothesis value, based on the direction specified in the alternative hypothesis.
• Describe how a two-tailed test is used in the context of comparing two independent population means.
  • When comparing two independent population means, a two-tailed test is used to determine if there is a significant difference between the means, without specifying the direction of the difference. The null hypothesis would state that the two population means are equal, while the alternative hypothesis would state that the means are not equal. The test statistic, such as the t-statistic, is then compared to the critical value from the appropriate t-distribution, with the critical region split into two tails. If the test statistic falls in the critical region, the null hypothesis is rejected, indicating a significant difference between the two population means.
• Explain how the choice between a two-tailed test and a one-tailed test can impact the results of hypothesis testing.
  • The choice between a two-tailed test and a one-tailed test can have a significant impact on the results of hypothesis testing. A two-tailed test is more conservative, as it requires a larger test statistic to reject the null hypothesis compared to a one-tailed test. This is because the critical region is split into two tails, reducing the probability of rejecting the null hypothesis in either direction. Conversely, a one-tailed test is more powerful, as it has a larger critical region in the direction specified by the alternative hypothesis. However, a one-tailed test also carries a higher risk of making a Type I error, as it increases the chances of rejecting the null hypothesis when it is true. The choice between a two-tailed or one-tailed test should be based on the research question and the specific alternative hypothesis being tested.

Related terms

Null Hypothesis: The null hypothesis is a statistical hypothesis that proposes that there is no significant difference between a sample statistic and a population parameter or between two population parameters.

Alternative Hypothesis: The alternative hypothesis is a statement that there is a significant difference between a sample statistic and a population parameter or between two population parameters.

One-Tailed Test: A one-tailed test is a statistical hypothesis test in which the critical region is located entirely in one tail of the sampling distribution, either above or below the null hypothesis value.