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Chi-Squared Goodness of Fit Tests With Applications [electronic resource]

V. Voinov, KIMEP University; Institute for Mathematics and Mathematical Modeling of the Ministry of Education and Science, Almaty, Kazakhstan, M. Nikulin, University Bordeaux-2, Bordeaux, France, N. Balakrishnan, McMaster University, Hamilton, Ontario, Canada
EBook; Book; Online
Amsterdam : Elsevier/AP, [2013]
9780123971944 (hardback)
"If the number of sample observations n ! 1, the statistic in (1.1) will follow the chi-squared probability distribution with r-1 degrees of freedom. We know that this remarkable result is true only for a simple null hypothesis when a hypothetical distribution is specified uniquely (i.e., the parameter is considered to be known). Until 1934, Pearson believed that the limiting distribution of the statistic in (1.1) will be the same if the unknown parameters of the null hypothesis are replaced by their estimates based on a sample; see, for example, Baird (1983), Plackett (1983, p. 63), Lindley (1996), Rao (2002), and Stigler (2008, p. 266). In this regard, it is important to reproduce the words of Plackett (1983, p. 69) concerning E. S. Pearson's opinion: "I knew long ago that KP (meaning Karl Pearson) used the 'correct' degrees of freedom for (a) difference between two samples and (b) multiple contingency tables. But he could not see that
Mode of access: World wide Web.
Includes bibliographical references (pages 215-226) and index.
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