Misconceptions about randomisation harm validity of randomised controlled trials.

Rationale: The coherence theory of truth, the epistemology of evidence-based medicine, mathematical statistics, and axiomatic mathematics.

Aims and objectives: To explore mathematical misconceptions inhering in randomised controlled trial designs, suggest improvements, encourage meta-methodological discussions and call for further interdisciplinary studies.

Method: Mathematical-statistical analyses and science-philosophical considerations.

Results: Randomisation does not (necessarily) generate equal samples, ergo, outcomes of usual RCTs are not as reliable as they claim. Moreover, ignoring initial sample discrepancies may cause inaccuracies similar to type I and type II errors. Insufficient awareness of these flaws harms final RCT statements about significance and evidence levels, hence their loss of trustworthiness. Statistical parameters such as the standard error of the mean may help to estimate the expected distinction between random samples.

Conclusion: Researchers in EBM should be aware of systemic misconceptions in RCT standards. Pre-measurement can reduce shortcomings, e.g. through calculation how sample differences impact on usual RCT processing, or randomisation is given up in favour of mathematical minimisation of sample differences, i.e. optimising statistical sample equality. Moreover, the promising future of dynamic simulation models is highlighted.