Comparing population distributions from bin-aggregated sample data: An application to historical height data from...

Area of Science:

• Statistics
• Demography
• Anthropometry

Background:

• Historical population data is often aggregated into bins due to confidentiality, limiting detailed analysis.
• Estimating continuous population distributions from binned data presents significant statistical challenges.

Observation:

• The study focuses on 19th-century French army conscript height data, available in binned format across 88 departments.
• This dataset allows for the comparison of full height distributions, accounting for potential measurement errors.

Findings:

• A novel methodology is presented to estimate continuous population distributions from bin-aggregated data.
• The approach utilizes mixture distribution models for maximal parametric flexibility.
• Statistical comparisons of height distributions across French departments are enabled through difference-of-means stochastic dominance tests.

Implications:

• This methodology offers a powerful tool for researchers working with aggregated or histogram-type data.
• It facilitates robust comparisons of population characteristics over time and across regions.
• The approach addresses limitations imposed by data aggregation, common in historical and sensitive datasets.