## 2 Background
### Using Response Times to Identify Rapid Guesses  
To address the problem of rapid guessing in low-stakes assessments, researchers often use RTs to identify students who answer the items too quickly, based on the assumption that each student needs a certain amount of time to read the item, understand what the item is asking, and provide an answer (e.g., selecting a response option in a multiple-choice item). To date, several RT-based methods have been proposed to detect rapid guessing (e.g., [5; 17; 17]). Typically, these methods rely on finding or setting a threshold based on the RT distribution of each item that categorizes responses as either rapid guessing (i.e., responses below the RT threshold) or solution behavior (i.e., responses above the RT threshold) and flags rapid guesses for removal (i.e., filtering) or further analysis [4].  
As there are no universally accepted rules for identifying a reasonable RT threshold, researchers implemented different criteria for the threshold-setting procedure, such as item characteristics (e.g., item difficulty), average or median RT values, and statistical characteristics of the RT distribution. For example, the visual inspection method [28; 29] assumes that if there is a significant amount of rapid guessing for an item, then the item's RT distribution should be bimodal, where the first mode represents rapid guesses and the second mode represents solution behaviors. A suitable threshold falling between the two modes can distinguish rapid guesses from the solution behavior. Despite its ease of use, this method becomes impractical when the item has a unimodal distribution, where RT values for rapid guesses and solution behavior are blended [7; 11].  
In this study, we propose a new approach for finding the optimal RT threshold in detecting rapid guessing by extending the two existing methods, namely the NT method [5] and the CUMP method [4]. The NT method identifies the RT threshold based on a user-defined percentage of the average RT value required to respond to an item (e.g., NT10 refers to 10% of the average RT value). The same percentage value (as seconds) is also used as the maximum value of the RT threshold. For example, if the average RT value for a given item is 50 s, then the RT threshold becomes 5 s (i.e., 10% of 50 s) based on the NT10 method. If, however, the resulting threshold was larger than 10 s, then the RT threshold would be 10 s. The same procedure can also be used with other percentage values (e.g.,15% for the NT15 method and 20% for the NT20 method). The NT method provides an easy and effective way to identify rapid guesses based on a user-defined criterion, instead of relying on visual inspection of a reasonable cut point in the RT distribution [5; 9].  
The CUMP method [4] sets the RT threshold by considering both the RT distribution of the item and the response accuracy among students who exhibit rapid guessing behavior. Specifically, this method assumes that students who rapidly guess the answer for a given item randomly select one of the response options, and thus the cumulative proportion-correct (i.e., response accuracy) for this group should be around the chance rate (e.g., 25% for an item with four response options). The authors in [4] argued that, as the duration spent on the item increases (i.e., transitioning to solution behavior), students' probability of answering the item correctly should go beyond the chance rate. Therefore, when the CUMP method is used, the threshold for detecting rapid guessing becomes the RT value for which the cumulative proportion-correct for students with rapid guessing is about to exceed the chance rate [4]. The CUMP method is more advantageous over other RT-based methods used for detecting rapid guessing because it relies on a mathematical definition instead of a visual inspection of the RT distribution. Moreover, the maximum RT threshold can be set based on statistical evidence from the RT distribution and the response accuracy [4; 9].