Two-Tailed Test

Definition

A two-tailed test is a statistical hypothesis test in which the critical region is two-sided, meaning it is located in both the upper and lower tails of the probability distribution. This type of test is used to determine if a parameter is significantly different from a hypothesized 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 researcher is interested in detecting a difference in either direction from the hypothesized value, rather than a specific direction.
2. The critical region in a two-tailed test is split equally between the upper and lower tails of the probability distribution, resulting in a smaller p-value for the same test statistic compared to a one-tailed test.
3. Two-tailed tests are commonly used in hypothesis testing for the mean, proportion, and correlation coefficient when the direction of the effect is not specified a priori.
4. The test statistic in a two-tailed test follows a symmetric probability distribution, such as the standard normal distribution (z-test) or the Student's t-distribution (t-test).
5. The choice between a one-tailed or two-tailed test depends on the research question and the researcher's prior expectations about the direction of the effect.

Review Questions

• Explain the purpose of a two-tailed test and how it differs from a one-tailed test.
  • The purpose of a two-tailed test is to determine if a parameter is significantly different from a hypothesized value, without specifying the direction of the difference. In a two-tailed test, the critical region is located in both the upper and lower tails of the probability distribution, whereas in a one-tailed test, the critical region is located in only one tail. This means that a two-tailed test is more appropriate when the researcher is interested in detecting a difference in either direction from the hypothesized value, rather than a specific direction.
• Describe the relationship between the critical region and the p-value in a two-tailed test.
  • In a two-tailed test, the critical region is split equally between the upper and lower tails of the probability distribution. This results in a smaller p-value for the same test statistic compared to a one-tailed test. The p-value in a two-tailed test represents the probability of obtaining a test statistic that is at least as extreme as the observed value, in either direction, under the assumption that the null hypothesis is true. The smaller the p-value, the stronger the evidence against the null hypothesis and the more likely the researcher is to reject it.
• Discuss the situations in which a two-tailed test would be more appropriate than a one-tailed test, and vice versa.
  • A two-tailed test is more appropriate when the researcher is interested in detecting a difference in either direction from the hypothesized value, and the direction of the effect is not specified a priori. This is common in hypothesis testing for the mean, proportion, and correlation coefficient. In contrast, a one-tailed test is more appropriate when the researcher has a specific directional expectation, such as testing if a new treatment is better than the control or if a parameter is greater than a hypothesized value. The choice between a one-tailed or two-tailed test depends on the research question and the researcher's prior expectations about the direction of the effect.

Related terms

One-Tailed Test: A one-tailed test is a statistical hypothesis test in which the critical region is located in only one tail of the probability distribution, either the upper tail or the lower tail.

Null Hypothesis: The null hypothesis is a statement about the value of a population parameter that the researcher tries to either support or reject based on sample data.

Alternative Hypothesis: The alternative hypothesis is a statement that the population parameter is different from the value specified in the null hypothesis.