The Effects of Misclassification Error on the Estimation of Several Population Proportions

Let us suppose that we observe a set of items which can be split into several distinct categories. Each item is measured and classified by some device into one of these various categories. However, the classified category for an item and the true category may not be the same, i.e., the device may make a misclassification error. The observed proportion of items in a category is then used to estimate the true proportion. The preceding scenario often occurs in quality control1 and medical research.2,3 In quality control, individual manufactured items from a sample or lot are often classified by a mechanical device as defective or not and the proportion of defectives in the sample is then used to estimate the proportion of defectives from the entire process. In medical research, the items are people and the idea is to estimate the proportion of people with various diseases. In a Bell system example, the items would be phone calls and the categories would be busies, completed calls, reorders, etc. An automated device would attempt to determine the true category for each call. The output of the device would then be the estimated proportion of calls in each category. This 697