Two-Sided Hypothesis

Definition

A two-sided hypothesis, also known as a two-tailed hypothesis, is a statistical hypothesis test where the null hypothesis states that the parameter of interest is equal to a specific value, and the alternative hypothesis states that the parameter is not equal to that value. This type of hypothesis test is used when the researcher is interested in detecting any difference, either positive or negative, between the parameter and the hypothesized value.

5 Must Know Facts For Your Next Test

1. In a two-sided hypothesis test, the alternative hypothesis states that the parameter is not equal to the value specified in the null hypothesis, meaning it could be either greater or less than the null value.
2. The two-sided hypothesis test is appropriate when the researcher is interested in detecting any significant difference, regardless of the direction, between the parameter and the hypothesized value.
3. The test statistic and p-value in a two-sided hypothesis test are calculated based on the absolute difference between the sample statistic and the hypothesized value, rather than the direction of the difference.
4. The significance level (α) is typically split equally between the two tails of the distribution, meaning that the critical values are determined using a significance level of α/2.
5. Two-sided hypothesis tests are commonly used in the context of comparing two population means with unknown standard deviations (topic 10.1) and in matched or paired samples (topic 10.4).

Review Questions

• Explain the purpose of a two-sided hypothesis test and how it differs from a one-sided hypothesis test.
  • The purpose of a two-sided hypothesis test is to determine if there is a significant difference, either positive or negative, between the parameter of interest and the value specified in the null hypothesis. This is in contrast to a one-sided hypothesis test, where the alternative hypothesis states that the parameter is either greater than or less than the null value, but not both. The two-sided test is appropriate when the researcher is interested in detecting any significant difference, regardless of the direction of the difference, whereas the one-sided test is used when the researcher has a specific directional expectation.
• Describe how the test statistic and p-value are calculated in a two-sided hypothesis test, and explain the significance level used.
  • In a two-sided hypothesis test, the test statistic and p-value are calculated based on the absolute difference between the sample statistic and the hypothesized value, rather than the direction of the difference. This is because the alternative hypothesis states that the parameter is not equal to the null value, which could be either greater or less than the null value. The significance level (α) is typically split equally between the two tails of the distribution, meaning that the critical values are determined using a significance level of α/2. This ensures that the overall probability of making a Type I error (rejecting the null hypothesis when it is true) is equal to the specified significance level.
• Explain how the two-sided hypothesis test is applied in the context of comparing two population means with unknown standard deviations (topic 10.1) and in matched or paired samples (topic 10.4).
  • In the context of comparing two population means with unknown standard deviations (topic 10.1), the two-sided hypothesis test is used to determine if there is a significant difference between the means of the two populations. The null hypothesis states that the two population means are equal, while the alternative hypothesis states that the means are not equal. This test is appropriate when the researcher is interested in detecting any significant difference, regardless of the direction of the difference. Similarly, in the context of matched or paired samples (topic 10.4), the two-sided hypothesis test is used to determine if there is a significant difference between the paired observations. The null hypothesis states that the mean difference between the paired observations is zero, while the alternative hypothesis states that the mean difference is not equal to zero. Again, the two-sided test is appropriate when the researcher is interested in detecting any significant difference, either positive or negative, between the paired observations.

Related terms

Null Hypothesis: The null hypothesis, denoted as H0, is a statement that the parameter of interest is equal to a specific value. It is the hypothesis that the researcher is trying to disprove or fail to reject.

Alternative Hypothesis:

The alternative hypothesis, denoted as H1 or Ha, is a statement that the parameter of interest is not equal to the value specified in the null hypothesis. It is the hypothesis that the researcher is trying to provide evidence for.

One-Sided Hypothesis:

A one-sided hypothesis, also known as a one-tailed hypothesis, is a statistical hypothesis test where the alternative hypothesis states that the parameter of interest is either greater than or less than the value specified in the null hypothesis.