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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.
In statistics education, informal inferential reasoning (also called informal inference) refers to the process of making a generalization based on data (samples) about a wider universe (population/process) while taking into account uncertainty without using the formal statistical procedure or methods (e.g. P-values, t-test, hypothesis testing, significance test).
Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed.
Causal analysis is the field of experimental design and statistical analysis pertaining to establishing cause and effect. [1] [2] Exploratory causal analysis (ECA), also known as data causality or causal discovery [3] is the use of statistical algorithms to infer associations in observed data sets that are potentially causal under strict assumptions.
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 ...
Anthropological survey paper from 1961 by Juhan Aul from University of Tartu who measured about 50 000 people. In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concerns or logistical constraints.
Although analytical studies need to take into account the uncertainty due to sampling, as in enumerative studies, the attributes of the study design and analysis of the data primarily deal with the uncertainty resulting from extrapolation to the future (generalisation to the conditions in future time periods).
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.