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Noncentral F-distribution
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<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a> and <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the noncentral <i>F</i>-distribution is a <a href="/facts/Continuous_probability_distribution/EpsKKVRu">continuous probability distribution</a> that is a <a href="/facts/Noncentral_distribution/uWgoRYTm">noncentral generalization</a> of the (ordinary) <a href="/facts/F-distribution/XNuuJtWY"><i>F</i>-distribution</a>. It describes the distribution of the quotient (<i>X</i>/<i>n</i>1)/(<i>Y</i>/<i>n</i>2), where the numerator <i>X</i> has a <a href="/facts/Noncentral_chi-squared_distribution/saAcjyRh">noncentral chi-squared distribution</a> with <i>n</i>1 degrees of freedom and the denominator <i>Y</i> has a central <a href="/facts/Chi-squared_distribution/wYnWWgUe">chi-squared distribution</a> with <i>n</i>2 degrees of freedom. It is also required that <i>X</i> and <i>Y</i> are <a href="/facts/Statistical_independence/NUzQtnUL">statistically independent</a> of each other. </p><p>It is the distribution of the <a href="/facts/Test_statistic/IBwfN5Kx">test statistic</a> in <a href="/facts/Analysis_of_variance/HHR2jkDk">analysis of variance</a> problems when the <a href="/facts/Null_hypothesis/C8NwSE9J">null hypothesis</a> is false. The noncentral <i>F</i>-distribution is used to find the <a href="/facts/Statistical_power/5KU54nW1">power function</a> of such a test. </p>