Using the Center for Epidemiologic Studies Depression Scale (CES-D) to Classify Participants of a Questionnaire Survey with Regard to Their Individual Inclination to Respond at Random

In this study, the well-known CES-D depression scale was considered as a prototypical tool for assessing an individual’s inclination to respond at random. It was postulated that the set of the responses obtained from the participants of a questionnaire survey could be divided into three classes: the honest responses class; the pure random class, characterized by the same prob- ability of each admissible score; the smart random class, characterized by the same distribution of the probability of scores as in the honest responses class. A two-step classifying procedure was recommended. According to this procedure, the first step should be to separate the pure random responses from the others. As needed, at the second step the smart random responses should be separated from the honest responses. The CES-D scale consists of sixteen direct questions and four reverse questions, each question with four admissible score values, 0, 1, 2, or 3. The material for the analyses includes all of the 4 294 967 296 possible arrangements of the four scores for the sixteen direct questions, and all of the 256 arrangements of the four scores for the four reverse questions, and all of the possible 49 · 13 = 637 pairs of the possible values of the mean scores from the sixteen direct questions and from the four reverse questions, respectively. It was assumed, without loss of generality, that the honest responses to the sixteen direct questions lead to the resulting distribution: P = (8/16; 5/16; 2/16; 1/16), for a score equal to 0, 1, 2, or 3, respectively. The original iterative procedure was used to compute the exact distributions of the mean scores in the pure random class, and in the smart random class. The discriminant ability to dis- tinguish between the two classes was characterized with the Receiver Operating Characteristic (ROC) curve. In result, the excellent discriminant properties of the CES-D were confirmed. The area under the ROC curve was estimated equal to AUC = 0.98 with standard error SE = 0.004 for the screening of the pure random responses from all of the others, and equal to AUC = 0.87 with standard error SE = 0.006 for the purpose of distinguishing the smart random responses from the honest ones.