On the correlation between size and metric validity

Abstract

Empirical validation of code metrics has a long history of success. Many metrics have been shown to be good predictors of external features, such as correlation to bugs. Our study provides an alternative explanation to such validation, attributing it to the confounding effect of size. In contradiction to received wisdom, we argue that the validity of a metric can be explained by its correlation to the size of the code artifact. In fact, this work came about in view of our failure in the quest of finding a metric that is both valid and free of this confounding effect. Our main discovery is that, with the appropriate (non-parametric) transformations, the validity of a metric can be accurately (with R-squared values being at times as high as 0.97) predicted from its correlation with size. The reported results are with respect to a suite of 26 metrics, that includes the famous Chidamber and Kemerer metrics. Concretely, it is shown that the more a metric is correlated with size, the more able it is to predict external features values, and vice-versa. We consider two methods for controlling for size, by linear transformations. As it turns out, metrics controlled for size, tend to eliminate their predictive capabilities. We also show that the famous Chidamber and Kemerer metrics are no better than other metrics in our suite. Overall, our results suggest code size is the only “unique” valid metric.