Honors Statistics

study guides for every class

that actually explain what's on your next test

Two-Tailed Test

from class:

Honors Statistics

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.

congrats on reading the definition of Two-Tailed Test. now let's actually learn it.

ok, let's learn stuff

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.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides