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What is the relation and difference between repeated _measures design and longitudinal study?

The repeated measures design (also known as a within-subjects design) uses the same subjects with every condition of the research, including the control. For instance, repeated measures are collected in a longitudinal study in which change over time is assessed. Other studies compare the same measure under two or more different conditions. For instance, to test the effects of caffeine on cognitive function, a subject's math ability might be tested once after they consume caffeine and another time when they consume a placebo.

A longitudinal study is a correlational research study that involves repeated observations of the same variables over long periods of time

They look like the same from Wikipedia.

Thanks and regards!

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This may be a semantic issue, as I think the terminology is used a bit differently from field to field; however, most usage will separate the terms by considering a repeated measure design as $experimental$, opposed to a longitudinal study which is more often $observational$. So in the repeated measure design, there are proper controlled treatment groups but some effort must go into treating (or avoiding) autocorrelation. An elementary repeated measures analysis would be 'paired t-test' whereas more sophisticated analyses include the so-called Generalized Estimating Equations which estimates the parameters of a GLM in the presence of autocorrelation. In a longitudinal study, there are observations over time but no true experimental design or manipulation. So the study may be termed 'correlational', which is the critical word you see in the Wikipedia article. So basically, repeated measures design = experimental; longitudinal analyses = observational.

All the best.

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