Case-series: comparing patients with a KNOWN OUTCOME (disease) to others with the same disease and looking back to see if they were exposed... "Did 2 people with the same disease get it from the same place?"
Case-control: comparing patients with a KNOWN OUTCOME (disease) to others WITHOUT (control) the disease and looking back to see if they were exposed. (odds ratio)... "they are sick and you want to see if drinking the contaminated water caused it by comparing them to normal people."
Cohort: Comparing patients with a KNOWN EXPOSURE and moving forward with them (prospective) or looking back in time (retrospective) to see if they developed the outcome (disease). (relative risk)... "they all drank the contaminated water and you want to see if they are more likely to get the disease."
Correlation is a statistical analysis used when both the dependent and independent variables have quantitative measurement values.
I hope this is right and helps... :)
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