# Repeated Measure

Repeated measure analysis involves a ‘within subject’ design.  The true ‘within subject’ design in this repeated measure analysis is a design in which each subject is measured under each treatment condition.  Similar analyses include a repeated measures ANOVA, MANOVA, and dependent sample t-test, as well as the non-parametric Wilcoxon signed rank test.  The repeated measures design in this repeated measure analysis is a design in which each subject is measured at two or more points with respect to time.  The profile analysis design in this repeated measure analysis is that which involves the comparison of the scores of the different tests that are comparably scaled.

How do test scores differ between time 1 and time 2?

Did the treatment prove effective on test scores across high school students from 9th – 12th grade?

Assumptions:

One of the major assumptions of this type of repeated measure analysis is that of sphericity.  If this assumption of sphericity is violated, then the value of F statistic will come out with severely biased results.  In other words, if the assumption of sphericity is violated, then the researcher might end up committing Type I error.

There are options available for the researcher to override this violation of assumptions while performing this type of repeated measure analysis. The researcher can do an adjusted degree of freedom test or use the Green house-Geisser method to overcome the effects of violation.

Wilcoxon signed rank test is the appropriate non-parametric alternative.

This repeated measure analysis is applicable to those research situations that utilize these within

The repeated measure design mechanically removes the individual differences from the between treatments variability as the same subjects are being used in every condition. In the case of the ANOVA/MANOVA,  individual differences are removed from the denominator of the F-test.

The result obtained is a test statistic that is similar to the independent measures’ result, except that in the result, all the individual differences are removed.

The common technique for measuring an effect size in this type of repeated measure analysis is to compute the percentage of variance that has been explained by the treatment effects.  For a dependent sample t-test, the effect size is measured by cohen’s d.  For ANOVA/MANOVA,  the effect size is identified as parital eta squared.  The researcher should keep in mind that before computing the effect size it is necessary to eliminate the individual differences between the subjects.

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ANOVA