Observational study

In an observational study the researcher records variables as they already stand and imposes nothing. Nobody is assigned to a group. The groups are formed by what the subjects already do or already are, and that single fact is why the design cannot settle cause. A survey is an observational study run by asking a standard set of questions.

An employer finds that 200 of its 500 staff use a standing desk and 300 do not. The standing desk users report a mean of 3.1 days of back pain per month against 4.6 days for everyone else, a difference of 1.5 days. That difference is real and it is an association. It is not evidence that the desks did anything, because the staff sorted themselves, and whoever chose a standing desk may also be younger, more active, or in better health to begin with. Every one of those traits travels with the group.

So this sentence fails: "the study shows that standing desks reduce back pain." The version that survives is "staff who use standing desks reported fewer days of back pain than staff who do not." The verbs carry the whole difference. Notice too that the arrow could point the other way. If the staff with chronic pain were the ones who asked for standing desks, this same design would show an association for a reason that has nothing to do with the desks working.

The reason is specific enough to write down. A confounding variable is one whose effect on the response cannot be separated from the explanatory variable's, and an observational study contains no mechanism that balances them. Random assignment balances the extraneous variables nobody thought to measure, which is its entire purpose; statistical adjustment can only handle the ones that were measured and recorded. A larger observational study estimates the association more precisely and does not make it one bit more causal.

Random selection is still worth having here. It earns the right to generalize the association to the population sampled, which is a separate permission from causation and is worked out under scope of inference.