A Correlation Analysis between Halstead Complexity Measures and other Software Measures

Halstead Complexity Measures, proposed in 1977, analyze a software system independently of its underlying programming language (technology) based on the measures number of operators and operands. From these two measures, it calculates other measures namely vocabulary, length, volume, difficulty, programming effort, errors, and testing time. The problem, nevertheless, is that since then the Academy and Industry have been coming up with hundreds of new metrics that differ in their assertions and calculations. Therefore, the objective of this paper is to present a correlation analysis between the eleven Halstead measures and other 27 popular measures proposed over the decades (e.g., LOC, cyclomatic complexity, and efferent coupling) through the inspection of 97 open-source Java systems in order to (i) identify redundancy in measures and (ii) minimize the costs of monitoring and diagnosing software projects, facilitating the task of making measurements. As a result, we identified strong correlations between Halstead measures and other measures, mainly related to size such as quantity of methods, packages, attributes, etc. We also identified direct correlation of Halstead measurements with coupling measures named Afferent and Efferent Coupling, with values ranging from 0.802 to 0.931, which are quite close to the maximum value 1 for a correlation. These results demonstrate that-although there is no perfect correlation-there is enough correlation to hypothesize that there is an overlap of measures with different denominations whose measured results are equivalent.