[1] The burden of proof rests on the demonstrable application of the statistical method, the disclosure of the assumptions, and the relevance that the test has with respect to a genuine understanding of the data relative to the external world.
[1][2] A common demarcation between science and non-science is the hypothetico-deductive proof of falsification developed by Karl Popper, which is a well-established practice in the tradition of statistics.
Science cannot achieve absolute certainty nor is it a continuous march toward an objective truth as the vernacular as opposed to the scientific meaning of the term "proof" might imply.
[9] Using the scientific method of falsification, the probability value that the sample statistic is sufficiently different from the null-model than can be explained by chance alone is given prior to the test.
Most statisticians set the prior probability value at 0.05 or 0.1, which means if the sample statistics diverge from the parametric model more than 5 (or 10) times out of 100, then the discrepancy is unlikely to be explained by chance alone and the null-hypothesis is rejected.
The formula is read as the probability of the parameter (or hypothesis =h, as used in the notation on axioms) “given” the data (or empirical observation), where the horizontal bar refers to "given".
All that one does in science is assign degrees of belief..."[14]: 180 According to Popper, hypotheses that have withstood testing and have yet to be falsified are not verified but corroborated.
Some researches have suggested that Popper's quest to define corroboration on the premise of probability put his philosophy in line with the Bayesian approach.
In this context, the likelihood of one hypothesis relative to another may be an index of corroboration, not confirmation, and thus statistically proven through rigorous objective standing.
[6][15] "Where gross statistical disparities can be shown, they alone may in a proper case constitute prima facie proof of a pattern or practice of discrimination.
"[nb 1]: 271 Statistical proof in a legal proceeding can be sorted into three categories of evidence: Statistical proof was not regularly applied in decisions concerning United States legal proceedings until the mid 1970s following a landmark jury discrimination case in Castaneda v. Partida.
"The Supreme Court has stated that the degrees of rigor required in the fact finding processes of law and science do not necessarily correspond.
Despite the statistical demonstration of an increased probability of discrimination, the legal burden of proof (it was argued) had to be examined on a case-by-case basis.