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Multivariate small sample tests for two-way designs with applications to industrial statistics

Author

Listed:
  • Rosa Arboretti

    (Civil, Environmental and Architectural Engineering University of Padova)

  • Riccardo Ceccato

    (University of Padova)

  • Livio Corain

    (University of Padova)

  • Fabrizio Ronchi

    (University of Padova)

  • Luigi Salmaso

    (University of Padova)

Abstract

In this paper, we present a novel nonparametric approach for multivariate analysis of two-way crossed factorial design based on nonparametric combination applied to synchronized permutation tests. This nonparametric hypothesis testing procedure not only allows to overcome the shortcomings of MANOVA test like violation of assumptions such as multivariate normality or covariance homogeneity, but, in an extensive simulation study, reveals to be a powerful instrument both in case of small sample size and many response variables. We contextualize its application in the field of industrial experiments and we assume a linear additive model for the data set analysis. Indeed, the linear additive model interpretation well adapts to the industrial production environment because of the way control of production machineries is implemented. The case of small sample size reflects the frequent needs of practitioners in the industrial environment where there are constraints or limited resources for the experimental design. Furthermore, an increase in rejection rate can be observed under alternative hypothesis when the number of response variables increases with fixed number of observed units. This could lead to a strategical benefit considering that in many real problems it could be easier to collect more information on a single experimental unit than adding a new unit to the experimental design. An application to industrial thermoforming processes is useful to illustrate and highlight the benefits of the adoption of the herein presented nonparametric approach.

Suggested Citation

  • Rosa Arboretti & Riccardo Ceccato & Livio Corain & Fabrizio Ronchi & Luigi Salmaso, 2018. "Multivariate small sample tests for two-way designs with applications to industrial statistics," Statistical Papers, Springer, vol. 59(4), pages 1483-1503, December.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-018-1032-y
    DOI: 10.1007/s00362-018-1032-y
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    References listed on IDEAS

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    1. Bathke, Arne C. & Harrar, Solomon W. & Madden, Laurence V., 2008. "How to compare small multivariate samples using nonparametric tests," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4951-4965, July.
    2. Solomon Harrar & Arne Bathke, 2012. "Erratum to: A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1087-1087, October.
    3. Solomon Harrar & Arne Bathke, 2012. "A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 135-165, February.
    4. Viatcheslav Melas & Andrey Pepelyshev & Petr Shpilev & Luigi Salmaso & Livio Corain & Rosa Arboretti, 2015. "On the optimal choice of the number of empirical Fourier coefficients for comparison of regression curves," Statistical Papers, Springer, vol. 56(4), pages 981-997, November.
    5. Livio Corain & Luigi Salmaso, 2013. "Nonparametric permutation and combination‐based multivariate control charts with applications in microelectronics," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(4), pages 334-349, July.
    6. Fabrizio Ronchi & Luigi Salmaso & Mattia De Dominicis & Juergen Illert, 2017. "Optimal Designs to Develop and Support an Experimental Strategy on Innovation of Thermoforming Production Process," Statistica, Department of Statistics, University of Bologna, vol. 77(2), pages 109-131.
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    Cited by:

    1. Rui Wang & Xingzhong Xu, 2021. "A Bayesian-motivated test for high-dimensional linear regression models with fixed design matrix," Statistical Papers, Springer, vol. 62(4), pages 1821-1852, August.
    2. Stefano Bonnini & Getnet Melak Assegie & Kamila Trzcinska, 2024. "Review about the Permutation Approach in Hypothesis Testing," Mathematics, MDPI, vol. 12(17), pages 1-29, August.
    3. Zhidong Bai & Jiang Hu & Chen Wang & Chao Zhang, 2021. "Test on the linear combinations of covariance matrices in high-dimensional data," Statistical Papers, Springer, vol. 62(2), pages 701-719, April.

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