An Exponentially Weighted Moving Average Procedure for Detecting Back Random Responding Behavior

Abstract

Back random responding (BRR) behavior is one of the commonly observed careless response behaviors. Accurately detecting BRR behavior can improve test validities. Yu and Cheng (2019) showed that the change point analysis (CPA) procedure based on weighted residual (CPA-WR) performed well in detecting BRR. Compared with the CPA procedure, the exponentially weighted moving average (EWMA) obtains more detailed information. This study equipped the weighted residual statistic with EWMA, and proposed the EWMA-WR method to detect BRR. To make the critical values adaptive to the ability levels, this study proposed the Monte Carlo simulation with ability stratification (MC-stratification) method for calculating critical values. Compared to the original Monte Carlo simulation (MC) method, the newly proposed MC-stratification method generated a larger number of satisfactory results. The performances of CPA-WR and EWMA-WR were evaluated under different conditions that varied in the test lengths, abnormal proportions, critical values and smoothing constants used in the EWMA-WR method. The results showed that EWMA-WR was more powerful than CPA-WR in detecting BRR. Moreover, an empirical study was conducted to illustrate the utility of EWMA-WR for detecting BRR.