Parents of newborn babies were divided into three groups as part of an experiment to see if the age at which a baby first walks can be affected by special exercises. For simplicity we will call the groups Grp1, Grp2, and Grp3. This computer output compares Grp1 to Grp2:
t = 1.28, df = 9.35, p-value = 0.2301
This computer output compares Grp1 to Grp3:
t = 3.04, df = 8.66, p-value = 0.01453
It seems that we are being told that µ1 = µ2 and that µ1 ≠ µ2. This might lead us to think that µ2 ≠ µ3 However, when we conduct a test to compare Grp2 to Grp3 we get a large P-value:
t = 1.1, df = 7.65, p-value = 0.3042
All three t tests used a non directional alternative. Discuss how it is possible that the three tests, taken together, seem to say that µ1 = µ2 and µ2 = µ3 but µ1 ≠ µ3.