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Multiple-comparison ANOVA problems

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  Multiple-comparison ANOVA problems [ edit ] The  F -test in one-way analysis of variance ( ANOVA ) is used to assess whether the  expected values  of a quantitative variable within several pre-defined groups differ from each other. For example, suppose that a medical trial compares four treatments. The ANOVA  F -test can be used to assess whether any of the treatments are on average superior, or inferior, to the others versus the null hypothesis that all four treatments yield the same mean response. This is an example of an "omnibus" test, meaning that a single test is performed to detect any of several possible differences. Alternatively, we could carry out pairwise tests among the treatments (for instance, in the medical trial example with four treatments we could carry out six tests among pairs of treatments). The advantage of the ANOVA  F -test is that we do not need to pre-specify which treatments are to be compared, and we do not need to adjust for ...
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Legendre chi function

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  Legendre chi function 10 languages Article Talk Read Edit View history Tools From Wikipedia, the free encyclopedia In  mathematics , the  Legendre chi function  is a  special function  whose  Taylor series  is also a  Dirichlet series , given by � � ( � ) = ∑ � = 0 ∞ � 2 � + 1 ( 2 � + 1 ) � . As such, it resembles the Dirichlet series for the  polylogarithm , and, indeed, is trivially expressible in terms of the polylogarithm as � � ( � ) = 1 2 [ Li � ⁡ ( � ) − Li � ⁡ ( − � ) ] . The Legendre chi function appears as the  discrete Fourier transform , with respect to the order ν, of the  Hurwitz zeta function , and also of the  Euler polynomials , with the explicit relationships given in those articles. The Legendre chi function is a special case of the  Lerch transcendent , and is given by � � ( � ) = 2 − � � Φ ( � 2 , � , 1 / 2 ) . Identities [ edit ] � 2 ( � ) + � 2 ( 1 / � ) = � 2 4 − � � 2 ln ⁡ | � | . � � � � 2 ...
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