ABSTRACT
Described in this chapter is a 2-parameter statistical model for the binary task. It introduces the fundamental concepts of decision variable and decision threshold (the latter, denoted zeta, is one of the parameters of the model) that pervade this book. Varying experimental conditions, like disease prevalence, cost, and benefits of decisions, can induce the observer to alter the decision threshold. The other parameter is the separation mu of two unit variance normal probability density functions (pdfs). The normal distribution, and associated pdf and sampling from it, is illustrated with R-examples. Expressions for sensitivity and specificity are derived. The receiver-operating characteristic (ROC) plot of TPF vs. FPF is introduced. The area AUC under the ROC curve is a measure of performance that is independent of the decision threshold. It also avoids ambiguity associated with comparing pairs of sensitivity and specificity values. The meaning of mu as the perceptual signal-to-noise ratio (pSNR) is compared to an SNR parameter in computerized analysis of mammography phantom images (CAMPI). The concept of random sampling is introduced by examining the dependence of variability of the operating point on the numbers of cases. Expressions are derived for 95% confidence intervals on an operating point. An online appendix contains the second part of the R tutorial, and more complex examples of code to be used in this book.
