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Scientific evidence is evidence which serves to either support or counter a scientific theory or hypothesis. Such evidence is expected to be empirical evidence and in accordance with scientific method. Standards for scientific evidence vary according to the field of inquiry, but the strength of scientific evidence is generally based on the results of statistical analysis and the strength of scientific controls.
Principles of inference 
Scientific evidence is evidence that does not concede the dependence of the evidence on principles of inference. This allows the relevancy of observations to a hypothesis to be determined by examining the assumptions made.
A person’s assumptions or beliefs about the relationship between observations and a hypothesis will affect whether that person takes the observations as evidence. These assumptions or beliefs will also affect how a person utilizes the observations as evidence. For example, the Earth's apparent lack of motion may be taken as evidence for a geocentric cosmology. However, after sufficient evidence is presented for heliocentric cosmology and the apparent lack of motion is explained, the initial observation is strongly discounted as evidence.
When rational observers have different background beliefs, they may draw different conclusions from the same scientific evidence. For example, Priestley, working with phlogiston theory, explained his observations about the decomposition of mercuric oxide using phlogiston. In contrast, Lavoisier, developing the theory of elements, explained the same observations with reference to oxygen. Note that a causal relationship between the observations and hypothesis does not exist to cause the observation to be taken as evidence, but rather the causal relationship is provided by the person seeking to establish observations as evidence.
A more formal method to characterize the effect of background beliefs is Bayesian inference. In Bayesian inference, beliefs are expressed as percentages indicating one's confidence in them. One starts from an initial probability (a prior), and then updates that probability using Bayes' theorem after observing evidence. As a result, two independent observers of the same event will rationally arrive at different conclusions if their priors (previous observations that are also relevant to the conclusion) differ. However, if they are allowed to communicate with each other, they will end in agreement (per Aumann's agreement theorem).
The importance of background beliefs in the determination of what observations are evidence can be illustrated using deductive reasoning, such as syllogisms. If either of the propositions is not accepted as true, the conclusion will not be accepted either.
Utility of scientific evidence 
Philosophers, such as Karl R. Popper, have provided influential theories of the scientific method within which scientific evidence plays a central role. In summary, Popper provides that a scientist creatively develops a theory which may be falsified by testing the theory against evidence or known facts. Popper’s theory presents an asymmetry in that evidence can prove a theory wrong, by establishing facts that are inconsistent with the theory. In contrast, evidence cannot prove a theory correct because other evidence, yet to be discovered, may exist that is inconsistent with the theory.
Philosophic versus scientific views of scientific evidence 
The philosophical community has investigated the logical requirements for scientific evidence by examination of the relationship between evidence and hypotheses, in contrast to scientific approaches which focus on the candidate facts and their context. Bechtel, as an example of a scientific approach, provides factors (clarity of the data, replication by others, consistency with results arrived at by alternative methods and consistency with plausible theories) useful for determination of whether observations may be considered scientific evidence.
There are a variety of philosophical approaches to decide whether an observation may be considered evidence; many of these focus on the relationship between the evidence and the hypothesis. Carnap recommends distinguishing such approaches into three categories: classificatory (whether the evidence confirms the hypothesis), comparative (whether the evidence supports a first hypothesis more than an alternative hypothesis) or quantitative (the degree to which the evidence supports a hypothesis). Achinstein provides a concise presentation by prominent philosophers on evidence, including Carl Hempel (Confirmation), Nelson Goodman (of grue fame), R. B. Braithwaite, Norwood Russell Hanson, Wesley C. Salmon, Clark Glymour and Rudolf Carnap
Based on the philosophical assumption of the Strong Church-Turing Universe Thesis, a mathematical criterion for evaluation of evidence has been proven, with the criterion having a resemblance to the idea of Occam's Razor that the simplest comprehensive description of the evidence is most likely correct. It states formally, "The ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized." 
See also 
- Longino, Helen (March 1979). Philosophy of Science, Vol. 46. pp. 37–42.
- Thomas S. Kuhn, The Structure of Scientific Revolution, 2nd Ed. (1970).
- William Talbott "Bayesian Epistemology" Accessed May 13, 2007.
- Thomas Kelly "Evidence". Accessed May 13, 2007.
- George Kenneth Stone, "Evidence in Science"(1966)
- Karl R. Popper,"The Logic of Scientific Discovery" (1959).
- Reference Manual on Scientific Evidence, 2nd Ed. (2000), p. 71. Accessed May 13, 2007.
- Deborah G. Mayo, Philosophy of Science, Vol. 67, Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part II: Symposia Papers. (Sep., 2000), pp. S194.
- William Bechtel, Scientific Evidence: Creating and Evaluating Experimental Instruments and Research Techniques, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1 (1990) p. 561.
- Rudolf Carnap, Logical Foundations of Probability (1962) p. 462.
- Peter Achinstein (Ed.) "The Concept of Evidence" (1983).
- Paul M. B. Vitányi and Ming Li; "Minimum Description Length Induction, Bayesianism and Kolmogorov Complexity".