Statistical theory
provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of 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. 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. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find the best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures.
Apart from philosophical considerations about how to make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory, to utility theory, and to optimization.
Scope
Statistical theory provides an underlying rationale and provides a consistent basis for the choice of methodology used in applied statistics.
Modelling
Statistical models describe the sources of data and can have different types of formulation corresponding to these sources and to the problem being studied. Such problems can be of various kinds:
Sampling from a finite population
Measuring observational error and refining procedures
Studying statistical relations
Statistical models, once specified, can be tested to see whether they provide useful inferences for new data sets.
Data collection
Statistical theory provides a guide to comparing methods of data collection, where the problem is to generate informative data using optimization and randomization while measuring and controlling for observational error. Optimization of data collection reduces the cost of data while satisfying statistical goals, while randomization allows reliable inferences. Statistical theory provides a basis for good data collection and the structuring of investigations in the topics of:
Design of experiments to estimate treatment effects, to test hypotheses, and to optimize responses.
Begin with the source’s own compact description: “Statistical theory” is provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The dossier treats that line as a proposition to test through Statistical, theory and provides, not as a finished interpretation.
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Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Feb 9, 2025. The linked authority identifier is Q3551145. None of the 0 selected statements returned an explicit reference.
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This entry incorporates text from “Statistical theory” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.