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Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.
Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. [48] Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
Social statistics is the use of statistical measurement systems to study human behavior in a social environment. Statistical finance , an area of econophysics , is an empirical attempt to shift finance from its normative roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective ...
In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power among all possible tests of a given size α.For example, according to the Neyman–Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.
Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure ...
A theory of statistical inference was developed by Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) [2] and "A Theory of Probable Inference" (1883), [3] two publications that emphasized the importance of randomization-based inference in statistics.
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Publications by Fisher, like "Statistical Methods for Research Workers" in 1925 and "The Design of Experiments" in 1935, [8] contributed to the popularity of significance testing, which is a probabilistic approach to deductive inference.