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🎲intro to statistics review

Dependent t-test

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The dependent t-test, also known as the paired t-test, is a statistical hypothesis test used to compare the means of two related or matched samples. It is typically used when the same group of individuals is measured under two different conditions or at two different time points.

5 Must Know Facts For Your Next Test

  1. The dependent t-test is used when the samples are related, such as when the same individuals are measured under two different conditions or at two different time points.
  2. The dependent t-test assumes that the differences between the paired observations are normally distributed.
  3. The test statistic for the dependent t-test is calculated by dividing the mean difference between the paired observations by the standard error of the mean difference.
  4. The degrees of freedom for the dependent t-test is equal to the number of pairs minus one.
  5. The dependent t-test is used to determine whether the mean difference between the paired observations is significantly different from zero.

Review Questions

  • Explain the purpose of the dependent t-test and when it is appropriate to use it.
    • The dependent t-test is used to compare the means of two related or matched samples, such as when the same group of individuals is measured under two different conditions or at two different time points. It is appropriate to use the dependent t-test when the samples are not independent, and the goal is to determine whether the mean difference between the paired observations is significantly different from zero.
  • Describe the assumptions of the dependent t-test and how they differ from the assumptions of the independent t-test.
    • The dependent t-test assumes that the differences between the paired observations are normally distributed, whereas the independent t-test assumes that the two samples are independent and normally distributed. Additionally, the dependent t-test has one fewer degree of freedom than the independent t-test because it is comparing the means of two related samples rather than two independent samples.
  • Analyze the implications of violating the assumptions of the dependent t-test and how this might affect the interpretation of the results.
    • If the assumptions of the dependent t-test are violated, such as if the differences between the paired observations are not normally distributed, the results of the test may be inaccurate or misleading. This could lead to incorrect conclusions about the significance of the mean difference between the paired observations, potentially resulting in Type I or Type II errors. In such cases, alternative statistical tests, such as the Wilcoxon signed-rank test, may be more appropriate.