The Confounding Effect of Class Size on The Validity of Obje(11)

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variables, for instance, on age and sex. Matching ensures that the cases and controls are similar on the

matching variable and therefore this variable cannot be considered a causal factor in the analysis.

Alternatively, one can have an unmatched case-control study and control for confounding effects during

the analysis stage.

In an unmatched case-control study the determination of an association between the exposure (product

metric) and the disease (fault-proneness) proceeds by calculating a measure of association and

determining whether it is significant. For example, consider the following contingency table that is

obtained from a hypothetical validation study:

Fault PronenessCouplingHC

LCFaulty9119Not Faulty1991

Table 1: A contingency table showing the results of a hypothetical validation study.

For this particular data set, the odds ratio is 22.9 (see the appendix, Section 7, for a definition of the odds

ratio), which is highly significant, indicating a strong positive association between coupling and fault-

proneness.

2.2.2 The Potential Confounding Effect of Size

One important element that has been ignored in previous validation studies is the potential confounding

effect of class size. This is illustrated in Figure 2.

Figure 2: Path diagram illustrating the confounding effect of size.

The path diagram in Figure 2 depicts a classic text-book example of confounding in a case-control study 14[99][12]. The path (a) represents the current causal beliefs about product metrics being an antecedent

We make the analogy to a case-control study because it provides us with a well tested framework for defining and evaluating

confounding effects, as well as for conducting observational studies from which one can make stronger causal claims (if all known

confounders are controlled). However, for the sole purposes of this paper, the characteristics of a confounding effect have been

described and exemplified in [61] without resort to a case-control analogy.14

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