UN CO RR EC TE D PR OO F 1 An Empirical Exploration of the Distributions of the 2 Chidamber and Kemerer Object - Oriented Metrics 3 Suite 4

The object-oriented metrics suite proposed by Chidamber and Kemerer (CK) is a measurement 18 approach towards improved object-oriented design and development practices. However, existing studies 19 evidence traces of collinearity between some of the metrics and low ranges of other metrics, two facts which 20 may endanger the validity of models based on the CK suite. As high correlation may be an indicator of 21 collinearity, in this paper, we empirically determine to what extent high correlations and low ranges might be 22 expected among CK metrics. 23 To draw as much general conclusions as possible, we extract the CK metrics from a large data set (200 24 public domain projects) and we apply statistical meta-analysis techniques to strengthen the validity of our 25 results. Homogeneously through the projects, we found a moderate (~0.50) to high correlation (>0.80) between 26 some of the metrics and low ranges of other metrics. 27 Results of this empirical analysis supply researchers and practitioners with three main advises: a) to avoid the 28 use in prediction systems of CK metrics that have correlation more than 0.80 b) to test for collinearity those 29 metrics that present moderate correlations (between 0.50 and 0.60) c) to avoid the use as response in continuous 30 parametric regression analysis of the metrics presenting low variance. This might therefore suggest that a 31 prediction system may not be based on the whole CK metrics suite, but only on a subset consisting of those 32 metrics that do not present either high correlation or low ranges.