Question

5. A step-by-step hypothesis test for a repeated measures design Aa Aa E Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis Ho: D 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed. Complete the following table by calculating the differences and the squared differences: Difference Score Squared Difference Score (D2) Observation A B (D B A) 1 3 3 4 5 7 8 9 The mean difference score is M

Answer 1

Obs A B D = B - A D^2 d - d bar)^2 1 1 3 2 4 0.64 2 3 4 1 1 0.04 3 5 7 2 4 0.64 4 4 4 0 0 1.44 5 8 9 1 1 0.04 M_D = sigma di/n = 6/5 = 1.2 s = 1/n - 1 sigma (di - d)^-2 = squareroot 2.8/4 = 0.836660 S_MD = S/squareroot n = 0.836660/squareroot 5 = 0.374161 t = M_d - mu_d/0.374161 = 1.2 - 0/0.374161 = 3.21 df are n - 1 = 4 p - values = 0.01629 finally, sine the t - statistic falls out side the critical region, you can reject H_0