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Many-to-one comparison of nonlinear growth curves for Washington's Red Delicious apple

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  • Nairanjana Dasgupta
  • Monte J. Shaffer

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.

Suggested Citation

  • Nairanjana Dasgupta & Monte J. Shaffer, 2012. "Many-to-one comparison of nonlinear growth curves for Washington's Red Delicious apple," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1781-1795, April.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:8:p:1781-1795
    DOI: 10.1080/02664763.2012.683168
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    References listed on IDEAS

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    1. F. Bretz & J. C. Pinheiro & M. Branson, 2005. "Combining Multiple Comparisons and Modeling Techniques in Dose-Response Studies," Biometrics, The International Biometric Society, vol. 61(3), pages 738-748, September.
    2. Hester, Susan M. & Cacho, Oscar, 2003. "Modelling apple orchard systems," Agricultural Systems, Elsevier, vol. 77(2), pages 137-154, August.
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    1. Herberich Esther & Hassler Christine & Hothorn Torsten, 2014. "Multiple Curve Comparisons with an Application to the Formation of the Dorsal Funiculus of Mutant Mice," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 1-14, November.

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