UNDERSTANDING THE REPEATED-MEASURES ANOVAREPEATED MEASURES ANOVA – Analysis of Variance in which subjects are measured morethan once to determine whether statistically significant change has occurred, for example, fromthe pretest to the posttest. (Vogt, 1999)- REPEATED MEASURES (ANOVA) – An ANOVA in which subjects are measured two ormore times and the total variation is partitioned into three components: (1) variationamong individuals; (2) variation among test occasions; and (3) residual variation (Hinkle,Wiersma, & Jurs, 2003).REPEATED-MEASURES DESIGN – A research design in which subjects are measured two or moretimes on the dependent variable. Rather than using different subjects for each level of treatment,the subjects are given more than one treatment and are measured after each. This means that eachsubject will be its own control. This research design goes by several different names, includingwithin-subjects ANOVA, treatments-by-subjects ANOVA, randomized-blocks ANOVA, one-wayrepeated-measures ANOVA and correlated groups design. (Vogt, 1999)SPHERICITY ASSUMPTION – A statistical assumption important for repeated-measures ANOVAs.When it is violated, F values will be positively biased. Researchers adjust for this bias by raisingthe critical value of F needed to attain statistical significance. Mauchley’s test for sphericity isthe most common way to see whether the assumption has been met. (Vogt, 1999)RESIDUAL VARIATION – Variation not due to either individuals or test occasions in repeatedmeasures ANOVA (Hinkle, Wiersma, & Jurs, 2003).ANOVA: SIMPLE REPEATED MEASURES designs involve measuring an individual two or moretimes on the dependent variable. For example, a researcher may test the same sample ofindividuals under different conditions or at different times. These people’s scores comprisedependent samples. For example, learning experiments often involve measuring the samepeople’s performance solving a problem under different conditions. Such a situation is analogousto, and an extension of, the design in which the dependent-samples t test was applied. With theone-way repeated-measures designs, each subject or case in a study is exposed to all levels of aqualitative variable and measured on a quantitative variable during each exposure. Thequalitative variable is referred to as a repeated-measures factor or a within-subjects factor. Thequantitative variable is called the dependent variable.In repeated-measures analysis (also called a within-subjects analysis); scores for the sameindividual are dependent, whereas the scores for different individuals are independent.Accordingly, the partitioning of the variation in ANOVA needs to be adjusted so that appropriateF ratios can be computed. The total sums of squares (SST) is partitioned into three components:(1) the variation among individuals (SSI); (2) the variation among test occasions (SSO); and (3)the remaining variation, which is called the residual variation (SSRes). The mean squares forthese sources of variation are computed, as before, by dividing the sums of squares by theirappropriate degrees of freedom. The mean square for the residual variation (MSRes = SSRes/dfRes)is used as the error term (the denominator of the F ratio) for testing the effect of test occasion,which is the effect of primary interest. It must be noted that there is no appropriate error term fortesting the effect of differences among the individuals.To conduct a repeated-measures ANOVA in SPSS, we do not specify the repeated-measuresfactor and the dependent variable in the SPSS data file. Instead, the SPSS data file containsseveral quantitative variables. The number of quantitative variables is equal to the number oflevels of the within-subjects factor. The scores on any one of these quantitative variables are thescores on the dependent variable for a single level of the within-subjects factor. Although we donot define the within-subjects factor in the SPSS data file, we specify it in the dialog box for theGeneral Linear Model Repeated-Measures procedure. To define the factor, we give a name to thewithin-subjects factor, specify the number of levels of this factor, and indicate the quantitativevariables in the data set associated with the levels of the within-subjects factor.UNDERSTANDING ONE-WAY REPEATED-MEASURES ANOVAIn many studies using the one-way repeated-measures design, the levels of a within-subjectfactor represent multiple observations on a scale over time or under different conditions.However, for some studies, levels of a within-subjects factor may represent scores from differentscales, and the focus may be on evaluating differences in means among these scales. In such asetting the scales must be commensurable for the ANOVA significance tests to be meaningful.That is, the scales must measure individuals on the same metric, and the difference scoresbetween scales must be interpretable.In some studies, individuals are matched on one or more variables so that individuals within a setare similar on a matching variable(s), while individuals not in the same set are dissimilar. Thenumber of individuals within a set is equal to the number of levels of a factor. The individualswithin a set are then observed under various levels of this factor. The matching process for thesedesigns is likely to produce correlated responses on the dependent variable like those ofrepeated-measures designs. Consequently, the data from these studies can be analyzed as if thefactor is a within-subjects factor.SPSS conducts a standard univariate F test if the within-subjects factor has only two levels.Three types of tests are conducted if the within-subjects factor has more than two levels: thestandard univariate F test, alternative univariate tests, and multivariate tests. All three types oftests evaluate the same hypothesis – the population means are equal for all levels of the factor.The choice of what test to report should be made prior to viewing the results.The standard univariate ANOVA F test is not recommended when the within-subjects factor has more then two levels because on of its assumptions, the sphericityassumption is commonly violated, and the ANOVA F test yields inaccurate p values tothe extent that this assumption is