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I need help on the best approach to perform statistical analysis to find out if there are any discrepancies in these data-sets for my students (for five independent years - with each year representing a different cohort of students):

  1. I would like to compare their projects grades and final grades for each year

  2. I would like to compare their predicted grades and final grades for each year

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You seem to have repeated measures data (also called longitudinal data) with two measurements per individual. I would start out with visualization, see for instance Plotting and presenting longitudinal data, options? and search this site. Maybe start with some kind of line plots, if you could post your data (in a readable form ..., if you cant share the data, some mock-up) we could experiment.

Also see Best practice when analysing pre-post treatment-control designs. For better advice you need to tell us more.

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