## 1 Introduction  
The occlusion of visual items in 2D data visualization techniques is an old problem that has been observed in many studies presented in the literature [1; 2; 3]. The occlusion issue is generally exacerbated due to the visual space available to present the data and the amount of data to be displayed. Depending on the level of occlusion, the user's perception of visual data can be affected, causing data misinterpretation or even loss of relevant information [4]. Considering previous studies, it is possible to highlight that they have mainly focused on the issue of reducing the occlusion effect for visual items when using data visualization techniques [5; 6; 7]. Some solutions reported include random jitter [8], the transparency technique [9], layout reconfiguration [10], focus+context techniques [11], multiple views [12], etc. Studies within psychology indicate that humans have mechanisms for recognizing partially occluded objects even when reduced in size and with low resolution [13]. However, [PERSON] [14] demonstrated that the recognition capacity of human beings decreases at higher levels of occlusion. Some research outside psychology has also suggested limits for occlusion levels that are tolerable for the human brain in efficiently detecting and identifying partially overlapped visual elements [2]. In general, clues about the efficiency and effectiveness of partially occluded visual variables in information visualization are split across multiple articles, making it difficult to compare and use the correct visual variable for a given data visualization scenario. Thus, this paper aims to present a comparative study of the perception of partially occluded visual variables in data visualization techniques, indicating how much the visual variable can be occluded and how many values it can encode in this condition. The results can be used as a set of good practices to apply visual variables in scenarios where occlusion is unavoidable,to increase the visual items in a data visualization technique, or even to provide indicators to compose quality criteria to evaluate data visualization techniques concerning the perception of their visual items. It should be noted that this study is an extension of research presented by [PERSON] [15], in which the preliminary tests and initial results presented in the previous analysis are described in detail. The comparative study proposal with regard to partially occluded visual variables is based on the location tasks for a visual target [16], and focuses on categorical data representations, considering hue, lightness, saturation, shape, text, orientation, and texture visual variables. To support the comparative study, a computational application was developed to generate random grid layout scenarios with 160 positions (10 \(\times\) 16), where each grid element presents one encoded value (from 3 to 5 values) of one visual variable, including a gray square in the center of the grid element representing the level of partial overlap that should be applied to the visual item (0% (control), 50%, 60%, and 70%), with one visual target generated as the task aim. The test involved 48 participants organized into four groups of 12 participants with 126 tasks per participant; the application captured the response and time for each task performed. The results analysis indicated that the hue, lightness, and shape visual variables maintained good accuracy and time performance for location tasks, even with 70% partial overlap and five values encoded. For the text and texture visual variables, the results showed good accuracy for partial overlap until 60% and until four values were encoded; the time performance of the text visual variable was a little better compared to the texture variable. For the 50% partial overlapping and three values encoded scenario only, the saturation variable showed good accuracy and time performance.