Answer is controlled trial.
There are three criteria for controlled trial . = randomization in sampling allocation, control group to compare the result, manipulation - here planned interventions of Mediterranean diet. All three are followed.
In this study participants are selected and assigned to each group, there is a control group( low fat diet) for doing comparison, planned interventions are carried out to one experimental group with Mediterranean Diet or Mediterranean Diet supplemented with nuts.
Other three are descriptive epidemiological study . No interventions are carried out.
Ecological studies are population based study. Instead of individual ,population shared same information are selected.
Case- control study- It is a descriptive analytical study. Used to study about rare diseases. Participants have a disease while enrolled into the research .They are considered as case and carefully analyses causes and route for disease occurrence. It is retrospective in nature.Individual had an exposure , but not having disease, taken as a control group.
e.g:people working in the chemical company have bladder cancer- case
people working in the chemical company have not bladder cancer- control
Cohort study-is also a descriptive analytical study. In which group of people with common characters are selected and conduct followup for finding outcome (occurrence of disease or event). It is longitudinal , prospective in nature.
e.g: adult having cigarette smoking for 10yrs( exposure) - case cohort - observe for outcome (occurrence of lung cancer and other events like Myocardial infarction, stroke, peripheral vascular diseases and so on.)
adult not having habit of cigarette smoking( no exposure)- control cohort- observe for occurrence of lung cancer and other events like Myocardial infarction, stroke, peripheral vascular diseases and so on.
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