The ability to effectively model and communicate the quality and uncertainty of the current result is an essential component of Progressive Data Analysis. By definition, the intermediate results that a PDA system displays during a computation are not yet complete, and so are estimates of the final result [8]. Users must be able to evaluate the PDA quality or PDA uncertainty of the intermediate results to make well-informed decisions. The user has to decide if the information computed and presented so far is close enough to the final result to make a decision, or if more time is needed. One of the main decisions that a user has to make is whether to act on an inter- mediate result or wait for the PDA to progress. Similar to Angelini et al. , we divide the process of a PDA analysis into three phases. In the first phase, the error ε due to PDA uncertainty is high, so the results are highly uncertain; there is a high risk when drawing any conclusion in this phase. In the second phase, intermediate results carry enough useful information to be interpreted. However, substantial PDA uncertainty remains and needs to be considered. During this phase, the user can make some predictions but cannot yet be sure of the results. In the third phase, the results are close to the final result, and further increases in quality will not influence the information carried by the results. The PDA uncertainty will not influence the analysis. In the final phase, the time spent on refinement can be considered wasted because there is no corresponding improvement in the results and uncertainty. An effective PDA uncertainty visualization both aids the user in determining the phase they are in and allows the user to assess the time needed to make well-informed decisions. PDA quality is used when we cannot model PDA uncertainty; it is a measure of the progress that indirectly relates to the quality of the results. While visualization has long grappled with the implications of uncertainty in data, PDA uncertainty and quality are intrinsic to PDA. By ignoring them, there is a real risk that users will make unfounded decisions based on premature results. For example, users might be tempted to stop progressivity at a point when the results confirm their own beliefs, but allowing the progression to run longer would have shown that the current result is an artifact. Conversely, users may take longer than needed to make good decisions if they cannot interpret the PDA uncertainty and quality correctly. Effective visualization of the PDA uncertainty and quality should aim at reducing or avoiding potential bias and errors as quickly as possible; the problem relates to the theory of sequential statistics and optimal stopping.