**6. Discussion**

When multiple views or complex graphical coding of multivariate data are used to bring loads of information into a single display, there is a considerable risk that the data representation will be visually impenetrable. Displays with multiple views can suffer from visual fragmentation, and perceptual interference can occur between different graphical codes in the same display (Healey, 2000; Bartram, 2001). The animated bubble charts presented in this article represent an attempt to simultaneously reduce visual fragmentation and perceptual interference.

Fig. 7. Two frames from an animation of score charts derived from a dataset containing information about the content of eight different fatty acids in olive oil from nine different

The technical performance of Excel-based animations is markedly influenced by the technique that is used to update the content of the worksheet cells. In particular, the computational time can be reduced considerably, if large arrays are updated by a single command rather than by creating a loop in which individual cells are updated one by one. The performance can also be improved by turning off the automatic screen updating and the automatic calculation of worksheets during parts of the execution of the animation

The design of the markers in the bubble chart is yet another factor that strongly influences the computational time. It takes longer to update large bubbles than small markers, and

Test runs using a dataset comprising 10,000 cases showed that a chart with 400 highlighted bubbles could be updated in less than two seconds on a standard PC. If the dataset is substantially larger, it may be preferable to base the animation on a (random) sample of the

When multiple views or complex graphical coding of multivariate data are used to bring loads of information into a single display, there is a considerable risk that the data representation will be visually impenetrable. Displays with multiple views can suffer from visual fragmentation, and perceptual interference can occur between different graphical codes in the same display (Healey, 2000; Bartram, 2001). The animated bubble charts presented in this article represent an attempt to simultaneously reduce visual fragmentation

more elaborate bubbles that resemble 3D balls can greatly retard the animation.

regions in Italy. Raw data were obtained from the Ggobi Website.

**5. Computational aspects** 

macro.

original data.

**6. Discussion** 

and perceptual interference.

The static background composed of open markers showing the distribution of the entire dataset enables rapid assessment of the distribution of a highlighted subset of data points. Moreover, the animation facilitates detection of change, because the analyst can inspect the shape and size of a highlighted point cloud while the previous point cloud is still fresh in memory.

Using filled markers of standardized shape makes it easier to discern the colour coding. Further, perception of a scatter plot can be strongly affected by the size of the markers, and hence it is worth noting that the built-in scaling feature in Excel can be used to reduce or increase the size of the bubbles in the charts. However, as emphasized in the introduction, only a few different colours and bubble sizes can be readily distinguished by visual inspection, and there may be perceptual interference between colour and size coding (Healey, 2000; Bartram, 2001). In addition, it should be mentioned that static visualizations, such as a small multiples display, are still viable alternatives to animated graphs (Robertson et al., 2008).

Much of the work presented here was inspired by Rosling and co-workers (Gapminder, 2011), who demonstrated that the animated bubble chart is a powerful tool for visualizing temporal trends in official statistics and other data collected annually for a set of objects. When one variable is plotted against another, and a video is created to simultaneously display changes over the period of data collection, the motion of the bubbles can draw attention to subsets of objects that move simultaneously in the same direction. Similarly, the motion makes it easier to identify deviating objects that move in a completely different direction.

Our work here has demonstrated that animated bubble charts are also very useful for inspecting temporal changes in the shape and size of 2D point clouds. For example, such animations can efficiently reveal changes in the presence of outliers or in the conditional mean and variance of one variable given another. Moreover, detection of change across time or groups can be greatly facilitated if open bubbles representing the entire dataset are allowed to form a static background, while selected subsets of data points are sequentially highlighted at a rate determined by the user.

Also, it should be noted that animated bubble charts can be useful, even if the order of the highlighted subsets lacks meaning. Without writing any computer code, a large number of simple bubble charts can be created and inspected at a pace determined by the analyst. Our animated 2D score charts represent yet another example of a time-saving procedure that can create a good overview of a complex dataset.

This article has focused on construction of animated bubble charts in a spreadsheet program where charts that are added are automatically updated when the contents of some worksheet cells are updated. Other software or programming environments can provide other solutions to animation problems. In R, for instance, a sequence of frames representing different time stamps are combined into a video prior to the animation, whereas the Google gadget *Motion Chart* provides several means of interaction. The main technical advantages offered by the Excel-based animations presented here are flexibility and the capacity to handle fairly large datasets. Test runs showed that, compared to Google *Motion Chart*, our tools can handle larger datasets. Furthermore, they are very flexible in three respects: (i) an arbitrary numerical or string variable can be used to determine the order in which different subsets of data are highlighted; (ii) any Excel tool can be used to modify the design of the bubble chart prior to the animation; (iii) multidimensional data can be scrutinized by first performing a principal components

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