# Everyone matters: h indices as new metrics for educational evaluation

## TL;DR

This paper introduces two new educational evaluation metrics, HEI and HLI, inspired by the h-index, to better capture group performance and score distribution.

## Contribution

The paper introduces HEI and HLI as novel metrics for educational evaluation that consider both overall performance and score distribution.

## Key findings

- HEI and HLI are easy to compute and provide richer data than average or median scores.
- HEI highlights high-scoring groups while HLI focuses on low-scoring groups, supporting equity analysis.
- The metrics are applicable beyond exams to any evaluation with continuous scores.

## Abstract

This paper addresses the limitations associated with using average scores for group evaluations. Drawing inspiration from the h-index in bibliometrics, we propose two new metrics for educational assessment: the h-efficiency index (HEI) and the h-loss index (HLI).

The HEI is defined such that among the scores of n subjects, if at most E% of all scores are at least E% of the maximum possible score, then the value of HEI is E%. In contrast, the HLI is defined so that among the scores of n subjects, if at most L% of all scores are no more than (100-L)% of the maximum score, then the value of HLI is L%. This paper employs course examination results as a case study to compare the evaluation outcomes of HEI and HLI with those of average scores and medians.

The findings demonstrate that HEI and HLI are straightforward to compute and serve as complementary metrics. They take into account not only the overall performance level but also the distribution of scores among the subjects. Compared to average and median scores, HEI and HLI provide richer and more informative data for comprehensive evaluations.

HEI emphasizes high-scoring groups, while HLI focuses on low-scoring groups, reflecting statistical robustness and aligning with the measurement needs of educational equality and equity. It is noteworthy that, although this analysis centers on examination results, the applicability of HEI and HLI extends to a broader range of contexts. These metrics can effectively measure any evaluation items with continuous scores and defined maximum and minimum values, providing a concise and efficient evaluation tool.