Sample size vs. bias in defect prediction

Most empirical disciplines promote the reuse and sharing of datasets, as it leads to greater possibility of replication. While this is increasingly the case in Empirical Software Engineering, some of the most popular bug-fix datasets are now known to be biased. This raises two significant concerns: first, that sample bias may lead to underperforming prediction models, and second, that the external validity of the studies based on biased datasets may be suspect. This issue has raised considerable consternation in the ESE literature in recent years. However, there is a confounding factor of these datasets that has not been examined carefully: size. Biased datasets are sampling only some of the data that could be sampled, and doing so in a biased fashion; but biased samples could be smaller, or larger. Smaller data sets in general provide less reliable bases for estimating models, and thus could lead to inferior model performance. In this setting, we ask the question, what affects performance more, bias, or size? We conduct a detailed, large-scale meta-analysis, using simulated datasets sampled with bias from a high-quality dataset which is relatively free of bias. Our results suggest that size always matters just as much bias direction, and in fact much more than bias direction when considering information-retrieval measures such as AUCROC and F-score. This indicates that at least for prediction models, even when dealing with sampling bias, simply finding larger samples can sometimes be sufficient. Our analysis also exposes the complexity of the bias issue, and raises further issues to be explored in the future.