Consider the following data from a matched pairs design. You want to use a matched pairs t-test to test the null hypothesis H₀: μ_D = 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five matched pairs, where the measurement from one member of the pair is labeled A, and the measurement from the other member of the pair is labeled B. Assume the population of the differences in these measurements is normally distributed.
Observation A B Difference Score (D = A - B) Deviation of the Difference Score (D - x̄_D) Squared Deviation of the Difference Score (D - x̄_D)²
The mean difference score is x̄_D =
Use x̄_D to complete the previous table by filling in the deviations of the difference scores and the squared deviations of the difference scores.
You want to test the null hypothesis that there are no differences in means between these two matched samples (H₀: μ_D = 0). To calculate the test statistic, you need to calculate the estimated standard deviation of the differences (s_D). The estimated standard deviation of the differences s_D = . The test statistic is t =
t Distribution
Degrees of Freedom = 7
You conduct a two-tail test at α = .05. To use the Distributions tool to find the critical values, you first need to set the degrees of freedom in the tool. The degrees of freedom are
The critical values (the values for t-scores that separate the tails from the main body of the distribution, forming the rejection region) are
Finally, since the t-statistic in the rejection region, you the null hypothesis.