Example 24. Repeated Measures Analysis: Exercise Data

In an exercise therapy study, three weight-lifting programs (PROG) are investigated: a control program (CONT), a program where the weight is increased (WI), and a program where the number of repetitions of each exercise is increased (RI). Several subjects are assigned to each group and each subject's strength (STRENGTH) is measured every other day for two weeks (S1-S7). The data is shown below.

Source:Littell, R.C., Freund, R.J. and Spector, P.C. (1991). SAS System for Linear Models. SAS Institute Inc.

Table 24: Exercise Data

SUBJ PROGRAM   S1   S2   S3   S4   S5   S6   S7

  1  CONT      85   85   86   85   87   86   87
  2  CONT      80   79   79   78   78   79   78
  3  CONT      78   77   77   77   76   76   77
  4  CONT      84   84   85   84   83   84   85
  5  CONT      80   81   80   80   79   79   80
  6  CONT      76   78   77   78   78   77   74
  7  CONT      79   79   80   79   80   79   81
  8  CONT      76   76   76   75   75   74   74
  9  CONT      77   78   78   80   80   81   80
 10  CONT      79   79   79   79   77   78   79
 11  CONT      81   81   80   80   80   81   82
 12  CONT      77   76   77   78   77   77   77
 13  CONT      82   83   83   83   84   83   83
 14  CONT      84   84   83   82   81   79   78
 15  CONT      79   81   81   82   82   82   80
 16  CONT      79   79   78   77   77   78   78
 17  CONT      83   82   83   85   84   83   82
 18  CONT      78   78   79   79   78   77   77
 19  CONT      80   80   79   79   80   80   80
 20  CONT      78   79   80   81   80   79   80
  1  RI        79   79   79   80   80   78   80
  2  RI        83   83   85   85   86   87   87
  3  RI        81   83   82   82   83   83   82
  4  RI        81   81   81   82   82   83   81
  5  RI        80   81   82   82   82   84   86
  6  RI        76   76   76   76   76   76   75
  7  RI        81   84   83   83   85   85   85
  8  RI        77   78   79   79   81   82   81
  9  RI        84   85   87   89   88   85   86
 10  RI        74   75   78   78   79   78   78
 11  RI        76   77   77   77   77   76   76
 12  RI        84   84   86   85   86   86   86
 13  RI        79   80   79   80   80   82   82
 14  RI        78   78   77   76   75   75   76
 15  RI        78   80   77   77   75   75   75
 16  RI        84   85   85   85   85   83   82
  1  WI        84   85   84   83   83   83   84
  2  WI        74   75   75   76   75   76   76
  3  WI        83   84   82   81   83   83   82
  4  WI        86   87   87   87   87   87   86
  5  WI        82   83   84   85   84   85   86
  6  WI        79   80   79   79   80   79   80
  7  WI        79   79   79   81   81   83   83
  8  WI        87   89   91   90   91   92   92
  9  WI        81   81   81   82   82   83   83
 10  WI        82   82   82   84   86   85   87
 11  WI        79   79   80   81   81   81   81
 12  WI        79   80   81   82   83   82   82
 13  WI        83   84   84   84   84   83   83
 14  WI        81   81   82   84   83   82   85
 15  WI        78   78   79   79   78   79   79
 16  WI        83   82   82   84   84   83   84
 17  WI        80   79   79   81   80   80   80
 18  WI        80   82   82   82   81   81   81
 19  WI        85   86   87   86   86   86   86
 20  WI        77   78   80   81   82   82   82
 21  WI        80   81   80   81   81   82   83

Questions:

1. Study the effect of the three programs on strength.

Keywords: Repeated measures, correlated measurements, sphericity test