Many-to-one comparison of nonlinear growth curves for Washington's Red Delicious apple |
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Authors: | Nairanjana Dasgupta Monte J. Shaffer |
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Affiliation: | 1. Department of Statistics , Washington State University , Pullman , WA , 99164-3144 , USA;2. McGuire Center for Entrepreneurship , University of Arizona , Tucson , AZ , 85721-0108 , USA |
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Abstract: | In this article, we are interested in comparing growth curves for the Red Delicious apple in several locations to that of a reference site. Although such multiple comparisons are common for linear models, statistical techniques for nonlinear models are not prolific. We theoretically derive a test statistic, considering the issues of sample size and design points. Under equal sample sizes and same design points, our test statistic is based on the maximum of an equi-correlated multivariate chi-square distribution. Under unequal sample sizes and design points, we derive a general correlation structure, and then utilize the multivariate normal distribution to numerically compute critical points for the maximum of the multivariate chi-square. We apply this statistical technique to compare the growth of Red Delicious apples at six locations to a reference site in the state of Washington in 2009. Finally, we perform simulations to verify the performance of our proposed procedure for Type I error and marginal power. Our proposed method performs well in regard to both. |
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Keywords: | multiple comparisons to control multivariate chi-square distribution nonlinear growth curves Richards’ curve simulated critical points |
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