Two-Tailed Test

Definition

A two-tailed test is a statistical hypothesis test in which the critical region is two-sided, meaning that the test statistic can fall in either the upper or lower tail of the distribution. This type of test is used to determine if a parameter is different from a specified value, without specifying the direction of the difference.

5 Must Know Facts For Your Next Test

1. In a two-tailed test, the null hypothesis is that the parameter is equal to a specified value, while the alternative hypothesis is that the parameter is not equal to that value.
2. The critical region for a two-tailed test is split evenly between the upper and lower tails of the distribution, with each tail containing half the significance level (α/2).
3. Two-tailed tests are commonly used when the researcher is interested in determining if a parameter is different from a specified value, but does not have a specific direction in mind for the difference.
4. Two-tailed tests are more conservative than one-tailed tests, as they require a larger test statistic to reject the null hypothesis and have a lower probability of Type I error.
5. The choice between a one-tailed or two-tailed test depends on the research question and the researcher's prior beliefs about the direction of the effect.

Review Questions

• Explain the purpose of a two-tailed test in the context of hypothesis testing.
  • The purpose of a two-tailed test is to determine if a parameter is different from a specified value, without specifying the direction of the difference. In a two-tailed test, the null hypothesis is that the parameter is equal to a specific value, and the alternative hypothesis is that the parameter is not equal to that value. This type of test is used when the researcher is interested in detecting any deviation from the null hypothesis, regardless of whether the parameter is greater or less than the specified value.
• Describe how the critical region is determined in a two-tailed test and how it differs from a one-tailed test.
  • In a two-tailed test, the critical region is split evenly between the upper and lower tails of the distribution, with each tail containing half the significance level (α/2). This means that the test statistic can fall in either the upper or lower tail of the distribution to reject the null hypothesis. In contrast, a one-tailed test has the entire critical region on one side of the distribution, either the upper or lower tail. The two-tailed test is more conservative than the one-tailed test, as it requires a larger test statistic to reject the null hypothesis and has a lower probability of Type I error.
• Analyze the relationship between the choice of a one-tailed or two-tailed test and the research question or the researcher's prior beliefs.
  • The choice between a one-tailed or two-tailed test depends on the research question and the researcher's prior beliefs about the direction of the effect. If the researcher has a specific hypothesis about the direction of the effect, a one-tailed test may be appropriate. However, if the researcher is interested in detecting any deviation from the null hypothesis, regardless of the direction, a two-tailed test is more appropriate. The two-tailed test is more conservative, as it requires a larger test statistic to reject the null hypothesis, but it also provides a more comprehensive evaluation of the research question by considering the possibility of both positive and negative deviations from the null hypothesis.

Related terms

Null Hypothesis: The null hypothesis is a statement about the value of a population parameter that the researcher believes is true and wants to test.

Alternative Hypothesis: The alternative hypothesis is a statement that contradicts the null hypothesis and represents the researcher's belief about the population parameter.

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