A General Analytic Method for Assessing Sensitivity to Bias of Performance Measures for Dichotomous Forecasts

Abstract

Performance measures computed from the 2 ? 2 contingency table of outcomes for dichotomous forecasts are sensitive to bias. The method presented here evaluates how the probability of detection (POD) must change as bias changes so that a performance measure improves at a given value of bias. A critical performance ratio (CPR) of the change of POD to the change in bias is derived for a number of performance measures. If a change in POD associated with a bias change satisfies the CPR condition, the performance measure will indicate an improved forecast. If a perfect measure of performance existed, it would always exhibit its optimal value at bias equal to one. Actual measures of performance are susceptible to bias, indicating a better forecast for bias values not equal to one. The CPR is specifically applied to assess the conditions for an improvement toward a more favorable value of several commonly used performance measures as bias increases or decreases through the value one. All performance measures evaluated are found to have quantifiable bias sensitivity. The CPR is applied to analyzing a performance requirement and bias sensitivity in a geometric model.