Metrics of color-difference formula improvement

Area of Science:

• Color Science
• Statistical Modeling
• Data Analysis

Background:

• Evaluating color-difference formulas relies on statistical metrics.
• Existing metrics like standardized residual sum of squares (SSS) and Pearson product moment correlation (PPMC) are used.
• Computational forms of these metrics depend on assumed linear data models.

Purpose of the Study:

• To demonstrate that SSS and PPMC metrics convey equivalent information.
• To highlight the importance of aligning computational forms with specific data models.
• To provide guidance on data preparation for accurate statistical analysis.

Main Methods:

• Comparative analysis of two computational forms for SSS and PPMC.
• Examination of linear data models with and without an ordinate intercept.
• Recommendation for explicit declaration of data centering (mean subtraction).

Main Results:

• SSS and PPMC metrics yield the same information regarding color-difference formula improvement.
• A mismatch between computational form and data model can lead to inaccurate results.
• Centering data aligns with the intercept-free model, simplifying analysis.

Conclusions:

• The choice of computational form for SSS and PPMC must match the data model.
• Explicitly stating whether data has been centered is recommended for clarity.
• Adherence to statistical assumptions (independence, normality, homogeneity) is vital for robust testing.