The 2 x 2 matrix format has been used in many different contexts when it comes to decision making. I have found the 2 x 2 matrix very useful in regulatory science especially when it comes to measuring regulatory compliance with rules. In this post, I would like to delineate how the 2 x 2 matrix can be used with nominal measurement of regulatory compliance where it is the essence of regulatory science metrics.
|Compliance (+)||Non-Compliance (-)|
|Measurement||Compliance (+)||(++) Expected||False Negative (-/+)|
|Non-Compliance (-)||False Positive (+/-)||(–) Expected|
In the 2 x 2 matrix above, the Regulatory Science Metrics Matrix, we are attempting to measure regulatory compliance comparing the measurement by an inspector with what exists in reality. The (+) = a positive response (there is compliance) and a (-) = a negative response (there is non-compliance). The (++) = compliance was recorded/measured and in reality there really was compliance. This is expected and desirable since we want everyone to comply with the respective rules we are measuring. The (–) = there was non-compliance recorded/measured and in reality there really was non-compliance. This is expected but not desirable; obviously we don’t want to find any non-compliance although it is good that the inspector is reliably accurate. The False Positive (+/-) = there was non-compliance recorded/measured but in reality there was compliance. The False Negative (-/+) = compliance was recorded/measured but in reality there was non-compliance.
From a regulatory science point of view and the measurement of regulatory compliance, the (++) and (–) are the two results we want to see; they are expected and desirable. We never want to see a False Negative (-/+), and we would like to minimize False Positives (+/-) whenever possible. In the actual regulatory science world, false positives and negatives do occur and are part of regulatory science. The goal is to minimize them as much as possible. This above Regulatory Science Metrics Matrix has become a useful tool in measuring regulatory compliance and in validation studies related to regulatory science in the human services.