Reproducibility is the ability to get the same research results or inferences, based on the raw data and computer programs provided by researchers. A related concept is replicability, meaning the ability to independently achieve non identical conclusions that are at least similar, when differences in sampling, research procedures and data analysis methods may exist. Reproducibility and replicability together are among the main beliefs of ‘the scientific method’ - with the concrete expressions of the ideal/idea of such a method varying considerably across research disciplines and fields of study .
The values obtained from distinct experimental trials are said to be commensurate if they are obtained according to the same reproducible experimental description and procedure. The basic idea can be seen in Aristotle's dictum that there is no scientific knowledge of the individual, where the word used for individual in Greek had the connotation of the idiosyncratic, or wholly isolated occurrence. Thus all knowledge, all science, necessarily involves the formation of general concepts and the invocation of their corresponding symbols in language (cf. Turner). Aristotle′s conception about the knowledge of the individual being considered unscientific is due to lack of the field of statistics in his time, so he could not appeal to statistical averaging by the individual.
A particular experimentally obtained value is said to be reproducible if there is a high degree of agreement between measurements or observations conducted on replicate specimens in different locations by different people—that is, if the experimental value is found to have a high precision. However, in science, a very well reproduced result is one that can be confirmed using as many different experimental setups as possible and as many lines of evidence as possible (consilience).
The first to stress the importance of reproducibility in science was the 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 e.g. 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.
Reproducibility is one component of the precision of a measurement or test method. The other component is repeatability which is the degree of agreement of tests or measurements on replicate specimens by the same observer in the same laboratory. Both repeatability and reproducibility are usually reported as a standard deviation. A reproducibility limit is the value below which the difference between two test results obtained under reproducibility conditions may be expected to occur with a probability of approximately 0.95 (95%).
Although they are often confused, there is an important distinction between replicates and an independent repetition of an experiment. Replicates are performed within an experiment. They are not and cannot provide independent evidence of reproducibility. Rather they serve as an internal "check" on an experiment and should not be shown as part of the experimental results within a scientific publication. It is the independent repetition of an experiment that serves to underpin its reproducibility 
The term reproducible research refers to the idea that the ultimate product of academic research is the paper along with the laboratory notebooks  and full computational environment used to produce the results in the paper such as the code, data, etc. that can be used to reproduce the results and create new work based on the research. Typical examples of reproducible research comprise compendia of data, code and text files, often organised around an R Markdown source document or a Jupyter notebook.
Psychology has seen a renewal of internal concerns about irreproducible results. Researchers showed in a 2006 study that, of 141 authors of a publication from the American Psychology Association (APA) empirical articles, 103 (73%) did not respond with their data over a 6-month period. In a follow up study published in 2015, it was found that 246 out of 394 contacted authors of papers in APA journals did not share their data upon request (62%). In a 2012 paper, it was suggested that researchers should publish data along with their works, and a dataset was released alongside as a demonstration, in 2017 it was suggested in an article published in Scientific Data that this may not be sufficient and that the whole analysis context should be disclosed. In 2015, Psychology became the first discipline to conduct and publish an open, registered empirical study of reproducibility called the Reproducibility Project. 270 researchers from around the world collaborated to replicate 100 empirical studies from three top Psychology journals. Fewer than half of the attempted replications were successful.
There have been initiatives to improve reporting and hence reproducibility in the medical literature for many years, which began with the CONSORT initiative, which is now part of a wider initiative, the EQUATOR Network. This group has recently turned its attention to how better reporting might reduce waste in research, especially biomedical research.
Reproducible research is key to new discoveries in pharmacology. A Phase I discovery will be followed by Phase II reproductions as a drug develops towards commercial production. In recent decades Phase II success has fallen from 28% to 18%. A 2011 study found that 65% of medical studies were inconsistent when re-tested, and only 6% were completely reproducible.
In 2012, a study by Begley and Ellis was published in Nature that reviewed a decade of research. That study found that 47 out of 53 medical research papers focused on cancer research were irreproducible. The irreproducible studies had a number of features in common, including that studies were not performed by investigators blinded to the experimental versus the control arms, there was a failure to repeat experiments, a lack of positive and negative controls, failure to show all the data, inappropriate use of statistical tests and use of reagents that were not appropriately validated. John P. A. Ioannidis writes, "While currently there is unilateral emphasis on 'first' discoveries, there should be as much emphasis on replication of discoveries." The Nature study was itself reproduced in the journal PLOS ONE, which confirmed that a majority of cancer researchers surveyed had been unable to reproduce a result.
In 2016, Nature conducted a survey of 1,576 researchers who took a brief online questionnaire on reproducibility in research. According to the survey, more than 70% of researchers have tried and failed to reproduce another scientist's experiments, and more than half have failed to reproduce their own experiments. "Although 52% of those surveyed agree there is a significant 'crisis' of reproducibility, less than 31% think failure to reproduce published results means the result is probably wrong, and most say they still trust the published literature."
Hideyo Noguchi became famous for correctly identifying the bacterial agent of syphilis, but also claimed that he could culture this agent in his laboratory. Nobody else has been able to produce this latter result.
In March 1989, University of Utah chemists Stanley Pons and Martin Fleischmann reported the production of excess heat that could only be explained by a nuclear process ("cold fusion"). The report was astounding given the simplicity of the equipment: it was essentially an electrolysis cell containing heavy water and a palladium cathode which rapidly absorbed the deuterium produced during electrolysis. The news media reported on the experiments widely, and it was a front-page item on many newspapers around the world (see science by press conference). Over the next several months others tried to replicate the experiment, but were unsuccessful.
Nikola Tesla claimed as early as 1899 to have used a high frequency current to light gas-filled lamps from over 25 miles (40 km) away without using wires. In 1904 he built Wardenclyffe Tower on Long Island to demonstrate means to send and receive power without connecting wires. The facility was never fully operational and was not completed due to economic problems, so no attempt to reproduce his first result was ever carried out.
Other examples which contrary evidence has refuted the original claim:
The reproducibility requirement cannot be applied to individual samples of phenomena which have a partially or totally non-deterministic nature. However, it still applies to the probabilistic description of such phenomena, with error tolerance given by probability theory.
It is interesting to note that at this moment of greater irreproducibility in life science, journals continue to minimize the space given to Materials and Methods sections in articles.