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In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions. It is a crucial step to test the original claim and confirm or reject the accuracy of results as well as for identifying and correcting the flaws in the original experiment. [1]
A random experiment is described or modeled by a mathematical construct known as a probability space. A probability space is constructed and defined with a specific kind of experiment or trial in mind. A mathematical description of an experiment consists of three parts: A sample space, Ω (or S), which is the set of all possible outcomes.
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.
Randomized, controlled, crossover experiments are especially important in health care. In a randomized clinical trial , the subjects are randomly assigned treatments. When such a trial is a repeated measures design, the subjects are randomly assigned to a sequence of treatments.
The Riemann Hypothesis. Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize ...
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [13] by Abraham Wald in the context of sequential tests of statistical hypotheses. [14]
A replication experiment to demonstrate that the same findings can be obtained in any other place by any other researcher is conceived as an operationalization of objectivity. It is the proof that the experiment reflects knowledge that can be separated from the specific circumstances (such as time, place, or persons) under which it was gained. [11]
When we repeat an experiment, as the saying goes, we really perform another experiment with a (more or less) similar set of generating conditions. To say that a set of generating conditions has propensity p of producing the outcome E means that those exact conditions, if repeated indefinitely, would produce an outcome sequence in which E ...
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