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Data quality is an important topic for many fields because real-world data is rarely perfect. Analysis conducted on data of variable quality can lead to inaccurate or incorrect results. To avoid this problem, researchers have introduced visual elements and attributes into traditional visualization displays to represent data quality information in conjunction with the original data. However, little work thus far has focused on creating an interactive interface to enable users to explicitly explore that data quality information. In this paper, we propose a framework for the linkage between data space and quality space for multivariate visualizations. Moreover, we introduce two novel techniques, quality brushing and quality-series animation, to help users with the exploration of this linkage. A visualization technique specifically designed for the quality space, called the quality map, is proposed as a means to help users create and manipulate quality brushes. We present some interesting case studies to show the effectiveness of our approaches.