The purpose of both the independent samples t-test and paired sample t-test is to analyze how closely related the two groups are to one another.

Question

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The independent samples t-test compares the means between two unrelated groups on the same continuous, dependent variable, while the paired sample t-test compares means from the same group at different times or under two different conditions, not how closely related the two groups are.

The Purpose of Both the Independent Samples T-Test and Paired