Repeated Measures

Statistics and Assumptions of Repeated Measures

As mentioned previously, the paired-sample t-test is a basic form of repeated measures design in that this analysis compares two points in time (e.g., before and after) using the same participants. Typically, repeated measures analysis is similar to an analysis of variance (ANOVA) in that researchers have an overall value that determines whether significance exists, and then they test differences between time periods using post-hoc analysis. More advanced designs might involve a pretest, immediate posttest, two-month delayed posttest, four-month delayed posttest, and so on. If researchers want to assess participants regularly over a long period of time (e.g., one year), a different type of statistical analysis—time-series analysis—may be warranted.

Repeated measures designs include the same assumptions of ANOVA, along with a new concern known as sphericity. Sphericity assumes that the correlations between values at the various times are roughly equal (or homogeneous). As an example, imagine that a financial adviser surveyed participants’ levels of confidence about money before, immediately after, one month after, and two months after a financial training session. In this case, sphericity assumes that the correlation between the baseline measurement and final measurement should be similar to the correlation between the middle two measurements. Put another way, researchers assume that the relationship between pairs of experimental conditions is similar, meaning that the level of dependence between pairs of groups is approximately equal. For sphericity to be an issue, researchers need to have at least three conditions, and with each additional factor, the risk for violating sphericity increases. Hence, if researchers analyze a repeated measures variable with only two levels, they do not need to be concerned with sphericity. Conversely, if researchers analyze a variable with eight levels, the risk for violating sphericity increases.

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