Hello Adesuwa,

The answer depends on: (a) what your research question is; (b) the experimental unit (is it individual cases, or is it groups); (c) the sampling design (are all cases independent, or are cases nested within larger subsets). In general, if there is any concern about (b) or (c), you may need to rely on mixed or hierarchical models in order to describe the phenomenon of interest accurately.

Finally, while averaged (grouped) data points can in fact yield different results than with individual data points and group averages tend not to vary as much as do individual scores, remember that you're no longer modeling the behavior of individual cases, but of batches of cases, and, the effective degrees of freedom will be fewer (hence, with potentially lower statistical power/precision).

Good luck with your work!

This is discussed in: Robinson W S 1950. Ecological correlations and the behavior of individuals. American Sociological Review 15: 351–57, where he discusses the ecological and atomistic fallacies, which is when you use the wrong level for the conclusion for the analyses that you did.

Individual.

Hope this helps,

Matt

This old (and rather faded) paper points out the difficulties in practice with analysing aggregates/averages and argues why you should consider multilevel models which allows you to get at averages but also a lot more

Article Variations in school examination performance: the applicatio...

You have a nice example where you should include "pure error" estimation. I agree with the Kelvyn's option of multilevel analysis if you have a clear idea about the aggregated units. Are you interested in the individual behaviour or in the aggregated behaviour modelling? if the aggregation is based only on the equal x values with no other meaning, I think it is better to work with individual values including pure error estimation.

Thank you everyone for your answers. Based on the insightful explanations given, and from the papers shared, I have decided to use the individual data.