Review of the methods of quantification

Area of Science:

• Statistics
• Data Analysis
• Psychometrics

Background:

• Qualitative data analysis often requires quantification for objective interpretation.
• Fisher, Guttman, and Hayashi proposed optimal scaling methods to assign scores to qualitative categories.
• Hayashi's quantification methods are widely utilized in Japan across social, marketing, psychological, and medical research.

Purpose of the Study:

• To provide a mathematical review of Hayashi's four quantification methods.
• To explore the application and limitations of these methods, particularly concerning ordered categories and statistical considerations.
• To highlight recent developments and available software for quantification analysis.

Main Methods:

• Review of Hayashi's four quantification methods.
• Categorization based on the presence or absence of an external criterion.
• Exploration of methods for ordered categories and statistical robustness.

Main Results:

• Hayashi's first and second methods are suitable for prediction and factor analysis with an external criterion.
• Hayashi's third and fourth methods are used for constructing spatial configurations to understand data relationships without an external criterion.
• Recent advancements address quantification for ordered categories and statistical considerations.

Conclusions:

• Hayashi's quantification methods offer versatile approaches for analyzing qualitative data.
• Further research and development are ongoing to enhance the application of these methods, especially for ordered data and statistical rigor.
• The review provides insights into practical applications and available computational tools.