Analysis of One-Way ANOVA Model using Synthetic Data

Biswajit Basak () and Bimal Sinha
Additional contact information
Biswajit Basak: Sister Nivedita University
Bimal Sinha: University of Maryland, Baltimore County

Sankhya B: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 7, 164-190

Abstract: 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.

Keywords: ANOVA problem; Non-central F distribution; Plug-in sampling; Posterior predictive sampling; Privacy protection (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13571-023-00318-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankhb:v:86:y:2024:i:1:d:10.1007_s13571-023-00318-4

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13571

DOI: 10.1007/s13571-023-00318-4

Access Statistics for this article

Sankhya B: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya B: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().