About: Checking whether a coin is fair

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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. The practical problem of checking whether a coin is fair might be considered as easily solved by performing a sufficiently large number of trials, but statistics and probability theory can provide guidance on two types of question; specifically those of how many trials to undertake and of the accuracy an estimate of the probability of turning up heads, derived from a given sample of trials.

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rdfs:label	Checking whether a coin is fair (en)
rdfs:comment	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. The practical problem of checking whether a coin is fair might be considered as easily solved by performing a sufficiently large number of trials, but statistics and probability theory can provide guidance on two types of question; specifically those of how many trials to undertake and of the accuracy an estimate of the probability of turning up heads, derived from a given sample of trials. (en)
foaf:depiction
dcterms:subject	Coin flipping Bayesian inference Experiments Statistical tests
Wikipage page ID	1604994 (xsd:integer)
Wikipage revision ID	1062050559 (xsd:integer)
Link from a Wikipage to another Wikipage	Bayesian inference Bayesian probability Margin of error Bayes' theorem Beta function Coin flipping Beta distribution Uniform distribution (continuous) Utility function Decision theory Point estimation Confidence interval Bayesian inference Estimation theory Coin Conjugate prior Credibility theory Statistical inference Experiments Bernoulli process Bernoulli trial Likelihood function Standard score Statistics Systematic bias Expected value Normal distribution Fair coin Probability density function Coin flip Probability theory Statistical randomness Statistical tests Binomial distribution Binomial test Coin flipping Dice Casino token Loss function Maximum a posteriori estimation Standard error Factorial Frequency probability Bayesian probability theory Abstain Prior distribution Inferential statistics Posterior distribution
sameAs	Checking whether a coin is fair Checking whether a coin is fair Checking whether a coin is fair Checking whether a coin is fair
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has abstract	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. The practical problem of checking whether a coin is fair might be considered as easily solved by performing a sufficiently large number of trials, but statistics and probability theory can provide guidance on two types of question; specifically those of how many trials to undertake and of the accuracy an estimate of the probability of turning up heads, derived from a given sample of trials. A fair coin is an idealized randomizing device with two states (usually named "heads" and "tails") which are equally likely to occur. It is based on the coin flip used widely in sports and other situations where it is required to give two parties the same chance of winning. Either a specially designed chip or more usually a simple currency coin is used, although the latter might be slightly "unfair" due to an asymmetrical weight distribution, which might cause one state to occur more frequently than the other, giving one party an unfair advantage. So it might be necessary to test experimentally whether the coin is in fact "fair" – that is, whether the probability of the coin's falling on either side when it is tossed is exactly 50%. It is of course impossible to rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping; also it is always possible for an unfair (or "biased") coin to happen to turn up exactly 10 heads in 20 flips. Therefore, any fairness test must only establish a certain degree of confidence in a certain degree of fairness (a certain maximum bias). In more rigorous terminology, the problem is of determining the parameters of a Bernoulli process, given only a limited sample of Bernoulli trials. (en)
gold:hypernym	Fair
prov:wasDerivedFrom	wikipedia-en:Checking_whether_a_coin_is_fair?oldid=1062050559&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Checking_whether_a_coin_is_fair
is Link from a Wikipage to another Wikipage of	Continuity correction Bernoulli process Fair coin Coin flipping List of statistics articles Checking if a coin be fair Checking if a coin is biased Checking if a coin is fair

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