Analysis of repeated measurements in physical therapy research: Multiple comparisons amongst level means and multi-factorial designs

This paper follows on from the previous article published in Physical Therapy in Sport (PtiS) on the analysis of repeated measurements (Atkinson, 2001). The aims are (i) to discuss more formal methods of making multiple comparisons amongst level means in a single factor and (ii) to describe the analysis of more complicated designs in physical therapy research, which may involve more than one factor of interest. Issues are discussed in parallel with the options for analysis that are available in the Statistical Package for the Social Sciences (SPSS). First, it is outlined how the hypothesis of interest and nature of the factor of interest (ordinal or nominal) governs how many multiple comparisons are made and whether multiple comparisons are needed at all. Next, it is explained why the sphericity assumption is just as important for making accurate multiple comparisons amongst level means as it is for the accuracy of the omnibus hypothesis test on the factor of interest. Using the results of statistical simulations, the relative merits of the different methods that are available for making multiple comparisons are then discussed. Next, the general problem that is associated with most multiple comparison procedures; relatively low statistical power, is highlighted and new stepwise correction procedures that are designed to overcome this problem of low power are introduced. Finally, the analysis and presentation of results for multifactorial designs is covered, including an explanation of what is considered to be the most complicated aspect of such analyses; the interpretation of a significant 'interaction' between factors.