Contents

408 PART V: Analyzing and Reporting ResearchTABLE 12.4DATA MATRIX AND ANALYSIS OF VARIANCE SUMMARY TABLE FOR A REPEATEDMEASURES 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.Source of Variation df SS MS F pSubjects 4 1553.5 — — —Interval length 3 2515.6 838.5 15.6 .000Residual (error variation) 12 646.9 53.9Total 19 4716.0The first step is to calculate a score to summarize each individual’s performancein each condition. In the time-perception experiment, participants experiencedeach condition six times; thus, with four conditions in the experiment,each participant made 24 estimates. A median was used to summarize eachparticipant’s performance in each of the four conditions. The next step in summarizingthe data is to calculate descriptive statistics across the participants foreach of the conditions. The means and standard deviations (in parentheses) foreach condition appear in Table 12.4. (See also Table 7.4).The focus of the analysis was on whether the participants could discriminateintervals of different lengths. The null hypothesis for an omnibus analysis ofvariance for the data in Table 12.4 is that the population means estimated foreach interval are the same. To perform an F-test of this null hypothesis, we needan estimate of error variation plus systematic variation (the numerator of anF-test). The variation among the mean estimates across participants for the fourintervals provides the information we need for the numerator. We know, thatif the different interval lengths did systematically affect the participants’ judgments,then the mean estimates for the intervals would reflect this systematicvariation. To complete the F-test, we also need an estimate of error variationalone (the denominator of the F-test). The source of variation in the repeated designis the differences in the ways the conditions affect different participants. Thisvariance estimate is called residual variation. See Box 12.4.Interpreting the ANOVA Summary Table The analysis of variance summary tablefor this analysis is presented in the lower portion of Table 12.4. The computations