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CHAPTER 7: Repeated Measures Designs 237All Possible Orders The preferred technique for balancing practice effects in theincomplete design is to use all possible orders of the conditions. Each participantis randomly assigned to one of the orders. With only two conditions thereare only two possible orders (AB and BA); with three conditions there are sixpossible orders (ABC, ACB, BAC, BCA, CAB, CBA). In general, there are N!(which is read “N factorial”) possible orders with N conditions, where N! equalsN(N 1) (N 2) . . . (N [N 1]). As we just saw, there are six possible orderswith three conditions, which is 3! (3 2 1 6). The number of required ordersincreases dramatically with increasing numbers of conditions. For instance, forfive conditions there are 120 possible orders, and for six conditions there are720 possible orders. Because of this, the use of all possible orders is usually limitedto experiments involving four or fewer conditions.Because there were four conditions in the Hansen et al. (2001) exercise experiment,24 sequences would be required to obtain all possible orders of conditions.These sequences (orders of conditions) are presented in the left half of Table 7.3.Using all possible orders certainly meets the general rule of ensuring that allconditions appear in each ordinal position equally often. The first ordinal positionshows this balancing most clearly: The first six sequences begin with the 0exercise condition, and each of the next six sets of sequences begins with oneof the three exercise conditions. The same pattern applies at each of the fourordinal positions. For example, the “0” condition also appears six times in thesecond ordinal position, six times in the third ordinal position, and six timesin the fourth ordinal position. The same is true for the 10-, 20-, and 30-minuteexercise conditions.TABLE 7.3ALTERNATIVE TECHNIQUES TO BALANCE PRACTICE EFFECTS IN AN INCOMPLETEREPEATED MEASURES DESIGN EXPERIMENT WITH FOUR CONDITIONSSelected OrdersRandom StartingAll Possible Orders Latin Square Order with RotationOrdinal Position Ordinal Position Ordinal Position Ordinal Position1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th 1st 2nd 3rd 4th0 10 20 30 20 0 10 30 0 10 20 30 10 20 30 00 10 30 20 20 0 30 10 10 30 0 20 20 30 0 100 20 10 30 20 10 0 30 30 20 10 0 30 0 10 200 20 30 10 20 10 30 0 20 0 30 10 0 10 20 300 30 10 20 20 30 0 100 30 20 10 20 30 10 010 0 20 30 30 0 10 2010 0 30 20 30 0 20 1010 20 0 30 30 10 0 2010 20 30 0 30 10 20 010 30 0 20 30 20 0 1010 30 20 0 30 20 10 0Note: The four conditions are identified using the time of exercise in the Hansen et al. (2001) experiment: 0 exercise, 10 minutes,20 minutes, and 30 minutes.