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Say that a study conducted included 300 type A blood cancer patients, 300 type B blood cancer patients, 300 type C blood cancer patients and 300 healthy people, all selected randomly from clinics' lists. We are then given the blood pressure of each patient and healthy person to check if there's a difference between the groups.

Would that be an observational study or experimental study? I'm leaning towards observational because we do not change anything, just "observe".

Also, why is the healthy 300 people that were randomly selected important for the study?

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Strictly speaking there isn't enough information to decide what study it is because the outcome(s) and exposure(s) have not been explicitly declared. If the different blood cancers are outcomes and blood pressure is exposure, then it's a case-control study design. However, it's silly because the different blood pressures can be a manifestation of the cancers so the outcome/exposure relationship can be mushy. Hence it's a funny design. In a way, it feels just like a cross-sectional survey.

Anyway, it's observational so far, because the researchers did not allocate exposures. Using "observing or not observing" as a criterion is risky because no matter what the researchers actually always observe, experimental or observational.

Random sampling is important because if the sample is not random, then all the statistical inferences based on the analysis will be challenged. In other words, a statistical test's result can be used to infer what happens in the population level because the sample was randomly chosen.

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