Paired t Test

The Paired t-Test examines repeated measurements obtained from the same set of individuals. The objective of the analysis is to show that any differences between two measurements of the same individuals are due to different treatment conditions. This approach is based on the theory that the same individuals will behave alike if they are treated alike and is frequently used in crossover studies. In this test, the variable of interest is the difference between the values of the individuals rather than the values themselves. Stated algebraically,

μD= Related values sample 1 – Related value sample 2


  • H0: μD = 0 (there is no difference between the two means)
  • H1: μD ≠ 0 (there is a difference between the two means)

Example: You might use the paired t-test to evaluate the efficacy of a femoral nerve block after a total knee replacement. Patients scheduled to have a bilateral knee replacement would have a femoral nerve block on one side and no nerve block on the other. At the conclusion of the study, the difference (μD) in morphine consumption after each knee replacement in each patient would be calculated. If a femoral nerve block were not efficacious, the patients would have no difference morphine consumption between sides (μD = 0). If it were efficacious, patients would consume less morphine when they got a nerve block (μD ≠ 0).

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