A randomized controlled trial (RCT) is a scientific study design used to evaluate the effectiveness of an intervention or treatment. In an RCT, participants are randomly assigned to either the treatment group or the control group, which helps eliminate bias and ensures that any differences in outcomes can be attributed to the intervention being studied rather than other factors.
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A randomized controlled trial assigns experimental units to competing treatments by a specified random mechanism and compares their outcomes. Under complete randomization of units, exactly receive assignment one and assignment zero. With fixed potential outcomes, each unit has assignment probability . ThereforeThis proves design-unbiasedness of the mean difference for the finite-population average treatment effect, assuming consistency in causal inference and no interference in causal inference.
Randomization controls the assignment distribution; it does not force every realized baseline covariate difference to be zero. Equal assignment probabilities yield unconditional exchangeability in the design, whereas covariate-dependent randomization can require conditional exchangeability and an analysis respecting that design.[ref]
Estimating causal effects from epidemiological data by Miguel A. Hernán and James M. Robins. Computation of causal effects via (conditional) randomisation: designs 1 and 2
When assigned and received treatments differ, an intention-to-treat analysis estimates an assignment-policy effect. A treatment-receipt effect needs additional assumptions. Allocation concealment, blinded outcome assessment and handling of missing follow-up address other sources of distortion beyond random assignment itself.