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CHAPTER 7: Repeated Measures Designs 241TABLE 7.4DATA MATRIX TABLE FOR A REPEATED MEASURES DESIGN EXPERIMENTData MatrixInterval LengthParticipant 12 24 36 481 13 21 30 382 10 15 38 353 12 23 31 324 12 15 22 325 16 36 69 60Mean (SD) 12.6 (2.0) 22.0 (7.7) 38.0 (16.3) 39.4 (10.5)Note: Each value in the table represents the median of the participants’ six responses at each level of theinterval length variable. The means in the bottom row are the averages of the medians (from six responsesmade by the five participants at each interval length).group’s performance; however, as this example illustrates, these summary statisticsalso can be used to represent one person’s performance when that performanceis an “average” across trials or tests.)Once an individual score for each participant in each condition has beenobtained, the next step is to summarize the results across participants, usingappropriate descriptive statistics. The mean estimate and standard deviation(SD) for each of the four intervals are listed in the row labeled “Mean (SD)”in Table 7.4. Even though the data for only five participants are included inthe table, these mean estimates indicate that participants appear to havediscriminated between intervals of different lengths, at least for intervals up to36 seconds.As we mentioned in Chapter 6, it is a good idea to include measures of effectsize when describing the results of an experiment. A typical measure ofeffect size for a repeated measures design is the strength of association measurecalled eta squared ( 2 ). The value of eta squared for the time-perceptionexperiment was .80. This value indicates that a large proportion of variationin participants’ time estimates can be accounted for by the independent variableof interval length. You can find more information about the calculationof effect sizes and their interpretation in Chapters 11 and 12. In Chapter 12we illustrate how to calculate eta squared using the data found in Table 7.4.Confirming What the Results Reveal• The general procedures and logic for null hypothesis testing and forconfidence intervals for repeated measures designs are similar to those usedfor random groups designs.Data analysis for experiments using repeated measures designs involves thesame general procedures we described in Chapter 6 for the analysis of randomgroups design experiments. Researchers use null hypothesis testing and