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A Family of Correlated Observations: From Independent to Strongly Interrelated Ones

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  • Daniel A. Griffith

    (School of Economic, Political and Policy Sciences, University of Texas at Dallas, Richardson, TX 75080, USA)

Abstract

This paper proposes a new classification of correlated data types based upon the relative number of direct connections among observations, producing a family of correlated observations embracing seven categories, one whose empirical counterpart currently is unknown, and ranging from independent (i.e., no links) to approaching near-complete linkage (i.e., n(n − 1)/2 links). Analysis of specimen datasets from publicly available data sources furnishes empirical illustrations for these various categories. Their descriptions also include their historical context and calculation of their effective sample sizes (i.e., an equivalent number of independent observations). Concluding comments contain some state-of-the-art future research topics.

Suggested Citation

  • Daniel A. Griffith, 2020. "A Family of Correlated Observations: From Independent to Strongly Interrelated Ones," Stats, MDPI, vol. 3(3), pages 1-19, June.
    • Handle: RePEc:gam:jstats:v:3:y:2020:i:3:p:14-184:d:378101
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    References listed on IDEAS

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    1. Blakeley B. McShane & David Gal & Andrew Gelman & Christian Robert & Jennifer L. Tackett, 2019. "Abandon Statistical Significance," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 235-245, March.
    2. Hodges, James S. & Reich, Brian J., 2010. "Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love," The American Statistician, American Statistical Association, vol. 64(4), pages 325-334.
    3. Daniel A. Griffith, 2019. "Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics," Stats, MDPI, vol. 2(3), pages 1-28, August.
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    Cited by:

    1. Daniel A. Griffith & Yongwan Chun & Monghyeon Lee, 2020. "Deeper Spatial Statistical Insights into Small Geographic Area Data Uncertainty," IJERPH, MDPI, vol. 18(1), pages 1-16, December.
    2. Daniel A. Griffith, 2023. "Understanding Spatial Autocorrelation: An Everyday Metaphor and Additional New Interpretations," Geographies, MDPI, vol. 3(3), pages 1-20, August.
    3. Daniel A. Griffith, 2022. "Selected Payback Statistical Contributions to Matrix/Linear Algebra: Some Counterflowing Conceptualizations," Stats, MDPI, vol. 5(4), pages 1-16, November.
    4. Daniel A. Griffith, 2021. "Articulating Spatial Statistics and Spatial Optimization Relationships: Expanding the Relevance of Statistics," Stats, MDPI, vol. 4(4), pages 1-18, October.
    5. Daniel A. Griffith & Richard E. Plant, 2022. "Statistical Analysis in the Presence of Spatial Autocorrelation: Selected Sampling Strategy Effects," Stats, MDPI, vol. 5(4), pages 1-20, December.

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