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Computational reproducibility means obtaining consistent results from the same input data, computational procedure and stated conditions. A reproducible analysis identifies the actual inputs and their data provenance, the software versions, parameters and relevant environment. Exact bitwise agreement is stronger than agreement within a justified numerical tolerance.^[ref]

For example, changing the order of a floating point sum can change its last few digits through rounding error. A useful check states the acceptable absolute error or relative error before comparing results. Successfully rerunning the same code also reruns any undetected mistake in it, so consistency is evidence about the computational process rather than a proof that the physical model is correct.

Scientific reproducibility concerns whether the basis of a scientific result can be reconstructed and checked. It requires enough information about the measurement, data handling and reasoning to distinguish repeating a procedure from merely obtaining a similar-looking answer.

Terminology varies between fields. The 2019 National Academies report distinguishes computational reproducibility, using the same data and computational procedure, from scientific replication, which collects new data to address the same scientific question. These test different links in the argument. Repeating a calculation can expose a software or transcription error; new observations can test whether the finding persists beyond the original sample.^[ref]

Consider an original toy measurement of three lengths, $10$, $11$ and $12$ units. Recomputing their arithmetic mean as $11$ checks the recorded calculation. Measuring three new objects tests a different question: whether the estimated mean describes further observations, allowing for measurement uncertainty and sampling variation. Neither exercise alone establishes that the instrument was correctly calibrated.