Repeated Measures Analysis of Variance

In a repeated measures analysis of variance, we are faced with the task of comparing means of groups that are dependent. Unlike the usual analysis of variance (ANOVA), where the groups are independent, in repeated measures ANOVA, the groups and the group means are dependent. Because the group means are dependent, we must adjust the usual statistical and inferential processes to take the dependencies into account. Before going on with our discussion of repeated measures ANOVAs, let's consider two situations that are likely to yield correlated means.

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To begin with, consider a situation in which we have 10 raters (judges) and five job applicants. In this situation, each rater would rate each candidate, but the five ratings generated by a rater are very likely to be dependent. If we were to create a table with candidates making the columns and raters making the rows, then the observations in each column would be independent, but not so across each row. The mean ratings for the candidates would then be dependent; comparing the means requires a procedure that takes into consideration the dependencies.

Consider another example where individuals are observed over time. In this type of experimental design, one or more groups of individuals are observed before and after a treatment. This design is traditionally called a pre-post design, and the number of posttreatment observations is usually greater than one. For instance, the individuals can be observed at 3-month intervals for a period of a year, yielding four posttreatment observations and one pretreatment observation. Just as in the previous example, these five means are likely to be correlated, and comparing them necessitates a procedure that takes the correlation into account.

We have seen two examples in which the means are probably dependent. However, there are many additional situations that can generate dependent means. For instance, using groups that have been matched along specific criteria to make them equivalent can also undermine the assumption of independence. Researchers must be vigilant and always look for design characteristics or constraints that may render the means dependent.

When repeated measures designs are compared to other designs, we see a number of advantages and disadvantages. Some of the advantages are that (a) they use fewer subjects; (b) they tend to be more efficient (subject variability is controlled better, which often increases power); and (c) they cost less to implement. Of course, not all studies can use repeated measures. There are many situations that preclude the use of repeated measures. For instance, if a prior treatment affects performance on a subsequent treatment—due to contrast effects, fatigue, emotional reaction, and so on—and one can't control for this nuisance effect, a repeated measures design would not be appropriate. (Keppel and Wickens have provided more information on nonstatistical problems that may affect the interpretation and execution of repeated measures studies.)

These advantages do not come without disadvantages. The major disadvantages of repeated measures designs are that they are harder to analyze and interpret. They are harder to analyze because the groups are not independent, and they are harder to interpret and design because of the possibility of carryover or similar effects.

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