Revisiting the relationship between fault detection, test adequacy criteria, and test set size

The research community has long recognized a complex interrelationship between fault detection, test adequacy criteria, and test set size. However, there is substantial confusion about whether and how to experimentally control for test set size when assessing how well an adequacy criterion is correlated with fault detection and when comparing test adequacy criteria. Resolving the confusion, this paper makes the following contributions: (1) A review of contradictory analyses of the relationships between fault detection, test adequacy criteria, and test set size. Specifically, this paper addresses the supposed contradiction of prior work and explains why test set size is neither a confounding variable, as previously suggested, nor an independent variable that should be experimentally manipulated. (2) An explication and discussion of the experimental designs of prior work, together with a discussion of conceptual and statistical problems, as well as specific guidelines for future work. (3) A methodology for comparing test adequacy criteria on an equal basis, which accounts for test set size without directly manipulating it through unrealistic stratification. (4) An empirical evaluation that compares the effectiveness of coverage-based testing, mutation-based testing, and random testing. Additionally, this paper proposes probabilistic coupling, a methodology for assessing the representativeness of a set of test goals for a given fault and for approximating the fault-detection probability of adequate test sets.