Statistical Methods for Evaluating Degradation Consistency

From Opinion to Statistics

Traditional authentication concludes with an expert's opinion: "consistent with the claimed date" or "inconsistent." While expert opinion is valuable, it is strengthened considerably when supported by statistical analysis.

The Basic Statistical Question

Given a textile claimed to be from a specific era and context:

• What is the expected range of degradation for genuine textiles of this type?
• Does the suspect textile fall within that range?

Building the Expected Range

From your database of verified genuine textiles, calculate:

For each dye type and age category:

• Mean degradation level (measured as ΔE from estimated original, or as specific spectral parameters)
• Standard deviation
• Range (minimum and maximum observed)

Example: For madder red on cotton, aluminum mordant, age 100-150 years, indoor display:

• Mean ΔE from estimated original: 12.4
• Standard deviation: 3.2
• Range: 6.8 - 19.1

A suspect textile claimed to be in this category with ΔE = 4.2 is well below the expected range (more than 2 standard deviations below the mean). This is statistically suspicious.

Confidence Intervals

Using the standard deviation of your reference data, establish confidence intervals:

• Within 1 SD of the mean (68% of genuine examples): Normal variation
• Within 2 SD (95%): Likely genuine, with some unusual but possible variation
• Beyond 2 SD (5%): Unusual — requires explanation
• Beyond 3 SD (0.3%): Highly unusual — strong indication of anomaly

Multivariate Analysis

A single measurement (e.g., overall ΔE) is less informative than multiple measurements:

• ΔE for red areas AND blue areas AND ground fabric
• Spectral comparison at multiple wavelengths
• Degradation pattern at multiple locations on the textile

Multivariate analysis tests whether all measurements fall within the expected multivariate range. A textile might have plausible individual measurements but an implausible combination.

Sample Size Limitations

Statistical analysis is only meaningful with adequate reference data. With fewer than 10 reference examples in a category, confidence intervals are wide and conclusions are tentative. This is why building the database (Blog Post 8) is so critical.

Presenting Statistical Results

In authentication reports, present statistical findings clearly:

• "The measured degradation falls 2.4 standard deviations below the mean for genuine textiles of this type and age, placing it at the 0.8th percentile."
• "This degree of deviation is observed in fewer than 1 in 100 genuine examples, suggesting the degradation is inconsistent with the claimed provenance."

This is more defensible than "it does not look right" and more persuasive in legal and scholarly contexts.

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