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Validation of Visual Statistical Inference, Applied to Linear Models

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  • Mahbubul Majumder
  • Heike Hofmann
  • Dianne Cook

Abstract

Statistical graphics play a crucial role in exploratory data analysis, model checking, and diagnosis. The lineup protocol enables statistical significance testing of visual findings, bridging the gulf between exploratory and inferential statistics. In this article, inferential methods for statistical graphics are developed further by refining the terminology of visual inference and framing the lineup protocol in a context that allows direct comparison with conventional tests in scenarios when a conventional test exists. This framework is used to compare the performance of the lineup protocol against conventional statistical testing in the scenario of fitting linear models. A human subjects experiment is conducted using simulated data to provide controlled conditions. Results suggest that the lineup protocol performs comparably with the conventional tests, and expectedly outperforms them when data are contaminated, a scenario where assumptions required for performing a conventional test are violated. Surprisingly, visual tests have higher power than the conventional tests when the effect size is large. And, interestingly, there may be some super-visual individuals who yield better performance and power than the conventional test even in the most difficult tasks. Supplementary materials for this article are available online.

Suggested Citation

  • Mahbubul Majumder & Heike Hofmann & Dianne Cook, 2013. "Validation of Visual Statistical Inference, Applied to Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 942-956, September.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:942-956
    DOI: 10.1080/01621459.2013.808157
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    Cited by:

    1. Andrew Zammit‐Mangion, 2020. "Discussion on A high‐resolution bilevel skew‐t stochastic generator for assessing Saudi Arabia's wind energy resources," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    2. Christina Korting & Carl Lieberman & Jordan Matsudaira & Zhuan Pei & Yi Shen, 2023. "Visual Inference and Graphical Representation in Regression Discontinuity Designs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(3), pages 1977-2019.
    3. Paul Blanche & Thomas A. Gerds & Claus T. Ekstrøm, 2019. "The Wally plot approach to assess the calibration of clinical prediction models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 150-167, January.
    4. Sayani Gupta & Rob J Hyndman & Dianne Cook, 2021. "Detecting Distributional Differences between Temporal Granularities for Exploratory Time Series Analysis," Monash Econometrics and Business Statistics Working Papers 20/21, Monash University, Department of Econometrics and Business Statistics.
    5. Jakob Peterlin & Nataša Kejžar & Rok Blagus, 2023. "Correct specification of design matrices in linear mixed effects models: tests with graphical representation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 184-210, March.
    6. Niladri Roy Chowdhury & Dianne Cook & Heike Hofmann & Mahbubul Majumder & Eun-Kyung Lee & Amy Toth, 2015. "Using visual statistical inference to better understand random class separations in high dimension, low sample size data," Computational Statistics, Springer, vol. 30(2), pages 293-316, June.

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