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Ordinal Level of Measurement

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The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
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Two-by-two ordinal patterns in art paintings.

Mateus M Tarozo1, Arthur A B Pessa1, Luciano Zunino2,3

  • 1Departamento de Física, Universidade Estadual de Maringá, Maringá, PR 87020-900, Brazil.

PNAS Nexus
|March 27, 2025
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Summary
This summary is machine-generated.

Researchers analyzed ordering patterns in pixel intensities across 140,000 paintings. Simple, universally applicable patterns reveal insights into artistic styles and their evolution over 1,000 years.

Keywords:
art historycomplexityesthetic measurespatial patterns

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Area of Science:

  • Computational art history
  • Digital humanities
  • Image analysis

Background:

  • Quantitative analysis of visual arts is expanding with digitized collections.
  • Understanding spatial structures is key, but defining simple, universal units is challenging.
  • Previous studies often lack universally applicable metrics for art analysis.

Purpose of the Study:

  • To develop universally applicable, interpretable units for analyzing paintings and artistic styles.
  • To investigate ordering patterns in pixel intensities across a large, diverse art dataset.
  • To establish a standardized metric for comparing artworks and tracking stylistic evolution.

Main Methods:

  • Analysis of ordering patterns in 2x2 pixel intensity partitions from ~140,000 digitized paintings.
  • Categorization of patterns into 11 types based on continuity and symmetry.
  • Statistical analysis of pattern distribution and prevalence across different art groups and time periods.

Main Results:

  • Identified 11 universal ordering pattern types applicable to paintings of any style or era.
  • Discovered a universal distribution of these patterns, modulated by pixel intensity relationships.
  • Demonstrated that these patterns correlate with low-level visual features and can identify painting styles.
  • Observed a trend of increasing divergence from average pattern prevalence over time, especially post-1930s.

Conclusions:

  • Ordinal patterns in pixel intensities offer a standardized, quantitative metric for art analysis.
  • These patterns provide insights into artistic style characteristics and their historical evolution.
  • Artworks show increasing stylistic divergence over time, with significant variability and non-uniform evolution.