Two-Sample T-Test

Definition

The two-sample t-test is a statistical hypothesis test used to determine if there is a significant difference between the means of two independent populations or groups. It is commonly used in the context of comparing the means of two samples to make inferences about the underlying populations.

5 Must Know Facts For Your Next Test

1. The two-sample t-test assumes that the two populations have equal variances (homogeneity of variance) and are normally distributed.
2. The test statistic for the two-sample t-test is calculated using the difference between the sample means, the standard errors of the means, and the degrees of freedom.
3. The null hypothesis for the two-sample t-test is that the means of the two populations are equal, while the alternative hypothesis is that the means are not equal.
4. The two-sample t-test can be used for both one-tailed and two-tailed tests, depending on the research question and the direction of the expected difference.
5. The choice between using a pooled or unpooled variance estimate in the two-sample t-test depends on the assumption of equal variances between the two populations.

Review Questions

• Explain the purpose of the two-sample t-test and the key assumptions required for its use.
  • The two-sample t-test is used to determine if there is a statistically significant difference between the means of two independent populations or groups. The key assumptions for using this test are that the two populations are normally distributed and have equal variances. These assumptions ensure the validity of the statistical inferences drawn from the test.
• Describe the difference between the null and alternative hypotheses in a two-sample t-test, and how the choice of a one-tailed or two-tailed test affects the interpretation of the results.
  • The null hypothesis for a two-sample t-test states that the means of the two populations are equal, while the alternative hypothesis states that the means are not equal. The choice of a one-tailed or two-tailed test depends on the research question and the expected direction of the difference. A one-tailed test is used when the researcher has a specific directional hypothesis, while a two-tailed test is used when the researcher is interested in any difference between the means, regardless of the direction.
• Explain how the choice between using a pooled or unpooled variance estimate in the two-sample t-test can impact the test results and the interpretation of the findings.
  • The choice between using a pooled or unpooled variance estimate in the two-sample t-test depends on the assumption of equal variances between the two populations. If the variances are equal (homogeneity of variance), a pooled variance estimate is used, which increases the statistical power of the test. If the variances are unequal, an unpooled variance estimate is used, which can lead to a different test statistic and potentially different conclusions about the significance of the difference between the means.

Related terms

Hypothesis Testing: The process of using statistical analysis to determine whether a claim or hypothesis about a parameter of a population is likely to be true or false.

Confidence Interval: A range of values that is likely to contain an unknown population parameter, with a specified degree of confidence.

Statistical Significance: The likelihood that an observed difference between two samples is due to chance, with a small p-value indicating a statistically significant difference.