Misclassification in 2 X 2 Tables

Although in the derivation of the chi-square test (and related techniques) the classifications in the 2 X 2 table are assumed to be correct, there are many practical problems where mistakes in classification are going to be made. The important question then arises: What effects will the misclassification have on conclusions drawn from the usual significance tests? The principal purpose of this paper is to answer this question. In the medical field there are some classifications that involve almost no risk of error, for example, the categories lived and died. On the other hand, in more complex diagnoses the clinician realizes that there is a considerable risk of error, a risk that may vary a great deal depending on the disease under study, the existence and availability of diagnostic tests, and other factors. For some diseases the principal misclassification will be in the direction of missing some of the actual cases. In other diseases there may be a risk of misdiagnosis in the other direction due to the existence of diseases which mimic the characteristics of the disease under study. Even when more precise classification is possible there may be time or cost factors that necessitate the use of cruder classification methods. In a large survey of mental health, for example, it will rarely be possible to have actual psychiatric diagnoses on all respondents. Instead it will be necessary to classify respondents as Problems or Not Health Problems on the basis of information in a question schedule. One possible procedure in such situations is to construct a mental health scale (using a subsample of problem and non-problem cases) and thereafter classify individuals by whether they fall above or below some critical point on the mental health scale. Such a procedure may well lead to appreciable misclassifications in both directions.