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• Noncentrality_parameter abstract "Noncentrality parameters are parameters of families of probability distributions that are related to other \"central\" families of distributions. Whereas the central distribution describes how a test statistic is distributed when the difference tested is null, noncentral distributions describe the distribution of a test statistic when the null is false. This leads to their use in statistics, especially calculating statistical power.If the noncentrality parameter of a distribution is zero, the distribution is identical to a distribution in the central family. For example, the Student's t-distribution is the central family of distributions for the Noncentral t-distribution family.Noncentrality parameters are used in the following distributions: Noncentral t-distribution Noncentral chi-squared distribution Noncentral chi-distribution Noncentral F-distribution Noncentral beta distributionIn general, noncentrality parameters occur in distributions that are transformations of a normal distribution. The \"central\" versions are derived from normal distributions that have a mean of zero; the noncentral versions generalize to arbitrary means. For example, the standard (central) chi-squared distribution is the distribution of a sum of squared independent standard normal distributions, i.e., normal distributions with mean 0, variance 1. The noncentral chi-squared distribution generalizes this to normal distributions with arbitrary mean and variance.Each of these distributions has a single noncentrality parameter. However, there are extended versions of these distributions which have two noncentrality parameters: the doubly noncentral beta distribution, the doubly noncentral F distribution and the doubly noncentral t distribution. These types of distributions occur for distributions that are defined as the quotient of two independent distributions. When both source distributions are central (either with a zero mean or a zero noncentrality parameter, depending on the type of distribution), the result is a central distribution. When one is noncentral, a (singly) noncentral distribution results, while if both are noncentral, the result is a doubly noncentral distribution. As an example, a t-distribution is defined (ignoring constant values) as the quotient of a normal distribution and the square root of an independent chi-squared distribution. Extending this definition to encompass a normal distribution with arbitrary mean produces a noncentral t-distribution, while further extending it to allow a noncentral chi-squared distribution in the denominator while produces a doubly noncentral t-distribution.Note also that there are some \"noncentral distributions\" that are not usually formulated in terms of a \"noncentrality parameter\": see noncentral hypergeometric distributions, for example.The noncentrality parameter of the t-distribution may be negative or positive while the noncentral parameters of the other three distributions must be greater than zero.".
• Noncentrality_parameter wikiPageExternalLink Comparison_of_noncentral_and_central_distributions.
• Noncentrality_parameter wikiPageID "20829683".
• Noncentrality_parameter wikiPageLength "3739".
• Noncentrality_parameter wikiPageOutDegree "22".
• Noncentrality_parameter wikiPageRevisionID "663540308".
• Noncentrality_parameter wikiPageWikiLink Category:Statistical_terminology.
• Noncentrality_parameter wikiPageWikiLink Chi-squared_distribution.
• Noncentrality_parameter wikiPageWikiLink Doubly_noncentral_t-distribution.
• Noncentrality_parameter wikiPageWikiLink Mean.
• Noncentrality_parameter wikiPageWikiLink Noncentral_F-distribution.
• Noncentrality_parameter wikiPageWikiLink Noncentral_beta_distribution.
• Noncentrality_parameter wikiPageWikiLink Noncentral_chi-squared_distribution.
• Noncentrality_parameter wikiPageWikiLink Noncentral_chi_distribution.
• Noncentrality_parameter wikiPageWikiLink Noncentral_hypergeometric_distributions.
• Noncentrality_parameter wikiPageWikiLink Noncentral_t-distribution.
• Noncentrality_parameter wikiPageWikiLink Normal_distribution.
• Noncentrality_parameter wikiPageWikiLink Probability_distribution.
• Noncentrality_parameter wikiPageWikiLink Statistical_power.
• Noncentrality_parameter wikiPageWikiLink Students_t-distribution.
• Noncentrality_parameter wikiPageWikiLink Variance.
• Noncentrality_parameter wikiPageWikiLinkText "Noncentrality parameter".
• Noncentrality_parameter wikiPageWikiLinkText "noncentrality parameter".
• Noncentrality_parameter wikiPageWikiLinkText "noncentrality".
• Noncentrality_parameter subject Category:Statistical_terminology.
• Noncentrality_parameter hypernym Parameters.
• Noncentrality_parameter comment "Noncentrality parameters are parameters of families of probability distributions that are related to other \"central\" families of distributions. Whereas the central distribution describes how a test statistic is distributed when the difference tested is null, noncentral distributions describe the distribution of a test statistic when the null is false.".
• Noncentrality_parameter label "Noncentrality parameter".
• Noncentrality_parameter sameAs Q7049207.
• Noncentrality_parameter sameAs m.05ztn14.
• Noncentrality_parameter sameAs Q7049207.
• Noncentrality_parameter wasDerivedFrom Noncentrality_parameter?oldid=663540308.
• Noncentrality_parameter isPrimaryTopicOf Noncentrality_parameter.