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The cumulative chi-squared method has been shown by Hirotsu (1979) and by Takeuchi & Hirotsu (1982) to have good power for testing against ordered alternatives in various statistical models. In this paper a related but simpler statistic is proposed. It is shown to have comparable power against ordered alternatives in analysis of variance models. The components of the statistic are optimal for testing deviations from the null hypothesis expressible in terms of Fourier cosine series. Both the new statistic and the cumulative chi-squared statistic are also shown to be Bayes tests.
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Vijay Nair (1986) studied this question.
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