3.16 Base rates and error rates

The base rate of a characteristic of interest is the probability of randomly selecting that specified characteristic from a relevant population. For example, in a population of 100 people 50 of whom have brown hair and 50 of whom have blonde hair, the base rate for brown hair is 0.5. The odds of brown:blonde hair are evens and so the prior odds of any one randomly selected individual having brown hair are evens. Base rates express prior probabilities/odds. In the context of diseases, the base rate is also known as the disease prevalence.

Error rates are used to quantify the uncertainty in making incorrect or inaccurate decisions and their exact definition depends upon context. An important context in forensic science is the error rate of binary decision: classifying a result as positive/negative, inclusion/exclusion, etc. In this context, the error rate describes the probability of making an incorrect classification. Error rates inform likelihood ratios.

Errors for binary classifications are often known as false positives and false negatives. If the truth is that there is a negative case, and it is mistakenly labelled as a positive case, then the assignment is a false positive. If the truth is that there is a positive case, and it is mistakenly labelled as a negative case, then the assignment is a false negative. If the classification is correct, then the assignment was a true positive or true negative, respectively. This information is presented in Table 3.1.

Table 3.1: Table 3.2: Labelling statistics based on the assigned label and the underlying truth.

Truth	Labelled positive	Labelled negative
Positive	<span style=” font-weight: bold; color: rgba(0, 114, 178, 255) !important;” >True positive</span>	<span style=” font-weight: bold; color: rgba(213, 94, 0, 255) !important;” >False negative</span>
Negative	<span style=” font-weight: bold; color: rgba(213, 94, 0, 255) !important;” >False positive</span>	<span style=” font-weight: bold; color: rgba(0, 114, 178, 255) !important;” >True negative</span>

If many assignments of positive/negative have been made under controlled conditions, e.g. when the underlying truth of positive or negative is known, then a reliable probability can be formed to determine the rate of true/false positives/negatives. These rates corresponds to the probability of each entry in Table 3.1 occurring. The probability of a false positive occurring is called the false positive rate and the probability of a false negative occurring is called the false negative rate. The probability of a true positive occurring is called the sensitivity and the probability of a true negative occurring is called the specificity.