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A theory of statistical inference was developed by Charles S. Peirce in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883), two publications that emphasized the importance of randomization-based inference in statistics.
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.
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.
He wrote a book entitled Manuscript on Deciphering Cryptographic Messages, containing detailed discussions on statistics and cryptanalysis. [2] [3] [4] Al-Kindi also made the earliest known use of statistical inference. [1] 13th century – An important contribution of Ibn Adlan was on sample size for use of frequency analysis. [1]
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 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.
Foundations of statistics involves issues in theoretical statistics, its goals and optimization methods to meet these goals, parametric assumptions or lack thereof considered in nonparametric statistics, model selection for the underlying probability distribution, and interpretation of the meaning of inferences made using statistics, related to the philosophy of probability and the philosophy ...
Statistics is the theory and application of mathematics to the scientific method including hypothesis generation, experimental design, sampling, data collection, data summarization, estimation, prediction and inference from those results to the population from which the experimental sample was drawn.