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Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. [ 1] 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.
Inferential statistics, which includes hypothesis testing, is applied probability. Both probability and its application are intertwined with philosophy. Philosopher David Hume wrote, "All knowledge degenerates into probability." Competing practical definitions of probability reflect philosophical differences.
Statistics (from German: Statistik, orig. "description of a state, a country") [ 1][ 2] is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. [ 3][ 4][ 5] In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or ...
Frequentist inference is a type of statistical inference based in frequentist probability, which treats “probability” in equivalent terms to “frequency” and draws conclusions from sample-data by means of emphasizing the frequency or proportion of findings in the data. Frequentist inference underlies frequentist statistics, in which the ...
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.
v. t. e. A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, [ 1] while descriptive statistics (in the mass noun sense) is the process of using and analysing those statistics. Descriptive statistics is distinguished from inferential ...
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. [ 1][ 2]
Classical inferential statistics emerged primarily during the second quarter of the 20th century, [6] largely in response to the controversial principle of indifference used in Bayesian probability at that time. The resurgence of Bayesian inference was a reaction to the limitations of frequentist probability, leading to further developments and ...