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The field of mathematical statistics was developed by Newton and Western mathematicians and originated in the 16th and early 17th centuries. Probability was first applied to collections of events in the 18th century by British mathematician John Bernoulli, who used Bernoulli trials as a model for many random phenomena (e.g., flipping a fair coin). The probability concept was used to design experiments and to illustrate the relationship between mathematical expectation (average) and variance.[7] The 19th-century French mathematician Émile Léonard Bernoulli established, for example, that the probability of an event is the ratio of the number of times that event occurs to the total number of possible outcomes.[21] In the 20th century, the conceptual and theoretical framework of probability was greatly expanded by axioms by axiomatic probability theory, while applications were greatly expanded by Monte Carlo methods and the development of probabilistic digital computers.
"In the separate-uncertainty framework, data are a sample drawn from an unknown population, and the goal of statistics is to draw inferences about properties of the population on the basis of that sample."[7] Data rarely, if ever, occur in isolation, that is, data are never observed without being related to a prior population; however, attributing significance to the data requires that we make the assumption that underlying some parameter values that are associated with the data. In their 1948 paper, Neyman and Pearson presented the first general definition of a statistical test, which comprised two parts: the null hypothesis and a measurable predicate of the sample under the null hypothesis. A test is a decision as to whether or not to reject the null hypothesis. A statistical test is a mathematical formula that involves data and can be applied to data to determine whether or not its assumption (the null hypothesis) is true. If the result of the test is insignificant (in that it indicates a low probability of the null hypothesis being true), then the null hypothesis is rejected and the null is not true. d2c66b5586
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