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Analysis of One-Way ANOVA Model using Synthetic Data

Author

Listed:
  • Biswajit Basak

    (Sister Nivedita University)

  • Bimal Sinha

    (University of Maryland, Baltimore County
    Center for Statistical Research and Methodology, U.S. Census Bureau)

Abstract

In this paper we consider the age-old ANOVA problem of testing the equality of means of several univariate normal populations with a common unknown variance, except that the data used for analysis arise from a synthetic version of the original observations. We address two versions of the synthetic data: one obtained under Plug-In sampling(PIS) method and the other under Posterior Predictive Sampling(PPS) method. We study its distributional properties (null and non-null) and provide enough computational details. A comparison of power is also provided. As expected, the power under the PIS method is more than that under the PPS method. A measure of privacy protection is also evaluated and it turns out that the PIS method provides less protection than the PPS method, thus confirming the standard belief that accuracy of inference and privacy protection work in opposite directions. Robustness of the proposed tests under deviations from normality is also studied.

Suggested Citation

  • Biswajit Basak & Bimal Sinha, 2024. "Analysis of One-Way ANOVA Model using Synthetic Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 164-190, May.
    • Handle: RePEc:spr:sankhb:v:86:y:2024:i:1:d:10.1007_s13571-023-00318-4
    DOI: 10.1007/s13571-023-00318-4
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    References listed on IDEAS

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    1. Satkartar K. Kinney & Jerome P. Reiter & Arnold P. Reznek & Javier Miranda & Ron S. Jarmin & John M. Abowd, 2011. "Towards Unrestricted Public Use Business Microdata: The Synthetic Longitudinal Business Database," International Statistical Review, International Statistical Institute, vol. 79(3), pages 362-384, December.
    2. Jerome P. Reiter, 2005. "Releasing multiply imputed, synthetic public use microdata: an illustration and empirical study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 185-205, January.
    3. Ali, Mukhtar M. & Sharma, Subhash C., 1996. "Robustness to nonnormality of regression F-tests," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 175-205.
    4. Ricardo Moura & Martin Klein & John Zylstra & Carlos A. Coelho & Bimal Sinha, 2021. "Inference for Multivariate Regression Model Based on Synthetic Data Generated Using Plug-in Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 720-733, April.
    5. Yehenew G. Kifle & Bimal K. Sinha, 2021. "Comparison of Some Exact Tests for a Common Location Parameter of Several Truncated Exponential Distributions with Different Scale Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 36-64, May.
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