Question

5. A step-by-step hypothesis test for a repeated-measures design

Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H0: μD=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:

Answer 1

Squared Differente Difference Srore (6B-A) observation A B 12 10 -2. 11 17 10 16 12 16 V 18 1 -1 1 2 Mo = SD - 2 + 1 - 1 + 1 +2 स MD = 0.2 for s let's make following table. e D-MD CD-MP)? CD-Mp3 observation -2 .2 6.89 0.8 0.64 - T -1.2 1:44 - 0:8 0 0.64 St.3.24 Total: 10.8

S = ECO-M2 nce 10.8 V4 V2.7 s = 1.643168 smo = 5 5 - 1.643168 rson lun = 0.734847 t = Hollo=0 Mp-up smp 0.2 -0 0.734847 0.734897 t = 0.27 degress of freedom & not where n is number of observations. nas i df = 4

Critical values &=0.05, df = 4 Critical values are, 0.025 0.025 - 2.7764, 2.7164. -2.7764 00:27 2 7764 The shaded region in above diagram is critical region. Finally, Since the t statistic do not falls in the Critical region you fail to reject the null hypothesis.