A Receiver Operating Characteristic (ROC) analysis is appropriate to a situation where a unit may be classified into one of two non-overlapping groups. The ROC curve is a plot of the false positive probability against the true positive probability. The area under the ROC curve measures the extent to which the variable under consideration can distinguish between the two groups. This thesis considers both the total area and partial area indices;The estimates of total and partial area are based on the observed data. Thus, when the variable being considered is measured with error, the added variability introduced by the measurement error causes bias in the estimates of total and partial area. This thesis considers the effects of nonsampling errors on the total and partial area indices, and develops bias-corrected estimates of total and partial area. The bias-corrected estimates provide a better measure of the ability of the underlying variable to distinguish between the two groups;The main focus of this thesis is on nonparametric methods of ROC analysis, but some common parametric models are considered also.