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In statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate basic ideas of statistical inference and, secondly, in providing a simple problem that can be used to compare various competing methods of statistical inference, including decision theory.
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 inferential statistics, a range of plausible values for some unknown parameter, such as a population mean, defined as an interval with a lower bound and an upper bound. [2] The precise values of these bounds are calculated from a pre-determined confidence level, chosen by the researcher. The confidence level represents the frequency of ...
The above image shows a table with some of the most common test statistics and their corresponding tests or models.. A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis.
Inverse probability, variously interpreted, was the dominant approach to statistics until the development of frequentism in the early 20th century by Ronald Fisher, Jerzy Neyman and Egon Pearson. [3] Following the development of frequentism, the terms frequentist and Bayesian developed to contrast these approaches, and became common in the 1950s.
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 .
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.
Statistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions.