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Reproducibility, closely related to replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated. There are different kinds of replication but typically replication studies involve different researchers using the same methodology. Only after one or several such successful replications should a result be recognized as scientific knowledge.

== History ==

The first to stress the importance of reproducibility in science was the Anglo-Irish chemist Robert Boyle, in England in the 17th century. Boyle's air pump was designed to generate and study vacuum, which at the time was a very controversial concept. Indeed, distinguished philosophers such as René Descartes and Thomas Hobbes denied the very possibility of vacuum existence. Historians of science Steven Shapin and Simon Schaffer, in their 1985 book Leviathan and the Air-Pump, describe the debate between Boyle and Hobbes, ostensibly over the nature of vacuum, as fundamentally an argument about how useful knowledge should be gained. Boyle, a pioneer of the experimental method, maintained that the foundations of knowledge should be constituted by experimentally produced facts, which can be made believable to a scientific community by their reproducibility. By repeating the same experiment over and over again, Boyle argued, the certainty of fact will emerge. The air pump, which in the 17th century was a complicated and expensive apparatus to build, also led to one of the first documented disputes over the reproducibility of a particular scientific phenomenon. In the 1660s, the Dutch scientist Christiaan Huygens built his own air pump in Amsterdam, the first one outside the direct management of Boyle and his assistant at the time Robert Hooke. Huygens reported an effect he termed "anomalous suspension", in which water appeared to levitate in a glass jar inside his air pump (in fact suspended over an air bubble), but Boyle and Hooke could not replicate this phenomenon in their own pumps. As Shapin and Schaffer describe, "it became clear that unless the phenomenon could be produced in England with one of the two pumps available, then no one in England would accept the claims Huygens had made, or his competence in working the pump". Huygens was finally invited to England in 1663, and under his personal guidance Hooke was able to replicate anomalous suspension of water. Following this Huygens was elected a Foreign Member of the Royal Society. However, Shapin and Schaffer also note that "the accomplishment of replication was dependent on contingent acts of judgment. One cannot write down a formula saying when replication was or was not achieved". The philosopher of science Karl Popper noted briefly in his famous 1934 book The Logic of Scientific Discovery that "non-reproducible single occurrences are of no significance to science". The statistician Ronald Fisher wrote in his 1935 book The Design of Experiments, which set the foundations for the modern scientific practice of hypothesis testing and statistical significance, that "we may say that a phenomenon is experimentally demonstrable when we know how to conduct an experiment which will rarely fail to give us statistically significant results". Such assertions express a common dogma in modern science that reproducibility is a necessary condition (although not necessarily sufficient) for establishing a scientific fact, and in practice for establishing scientific authority in any field of knowledge. However, as noted above by Shapin and Schaffer, this dogma is not well-formulated quantitatively, such as statistical significance for instance, and therefore it is not explicitly established how many times must a fact be replicated to be considered reproducible.

== Terminology == Replicability and repeatability are related terms broadly or loosely synonymous with reproducibility (for example, among the general public), but they are often usefully differentiated in more precise senses, as follows. Two major steps are naturally distinguished in connection with reproducibility of experimental or observational studies: when new data are obtained in the attempt to achieve it, the term replicability is often used, and the new study is a replication or replicate of the original one. Obtaining the same results when analyzing the data set of the original study again with the same procedures, many authors use the term reproducibility in a narrow, technical sense coming from its use in computational research. Repeatability is related to the repetition of the experiment within the same study by the same researchers. Reproducibility in the original, wide sense is only acknowledged if a replication performed by an independent researcher team is successful. The terms reproducibility and replicability sometimes appear even in the scientific literature with reversed meaning, as different research fields settled on their own definitions for the same terms.

== Measures of reproducibility and repeatability == In chemistry, the terms reproducibility and repeatability are used with a specific quantitative meaning. In inter-laboratory experiments, a concentration or other quantity of a chemical substance is measured repeatedly in different laboratories to assess the variability of the measurements. Then, the standard deviation of the difference between two values obtained within the same laboratory is called repeatability. The standard deviation for the difference between two measurement from different laboratories is called reproducibility. These measures are related to the more general concept of variance components in metrology.

== Reproducible research ==