# Hierarchical Association Coefficient Algorithm

## TL;DR

The paper introduces a new algorithm to measure how ordered data fits within stratified categories.

## Contribution

The Hierarchical Association Coefficient algorithm is proposed to quantify the proximity of ordered data to ideal sorting extremes.

## Key findings

- The HA-coefficient algorithm is grounded in theoretical principles of stratified categorization.
- Example data and simulations demonstrate the algorithm's practical utility and reliability.
- The algorithm can assess how close an observed order is to an ideal ascending or descending extreme.

## Abstract

Suppose that members in a universal set categorized based on observations, and that categories can be stratified based on the average of observations within each category. Two sorting extremes can be obtained from the perspective of arbitrariness of an order of observations. The first sorting extreme is an increasing order of observations on ascendingly stratified categories. The second sorting extreme is a decreasing order of observations on ascendingly stratified categories. Hierarchical association coefficient (HA-coefficient) algorithm is based on a principle that any order of observations in stratified categorization can be placed between the two sorting extremes. The algorithm produces a proportion of how much an order of observations in stratified categorization is close to the first sorting extreme, or how much an order of categorized observations is distant from the second sorting extreme. This paper introduces a theory about the HA-coefficient algorithm, and shows its applications with example data. In addition, proving a reliability of the algorithm is shown through a simulation.