**4.5 Score charts for a pair of principal components**

When the collected data are multivariate and the coordinates are strongly correlated, important information can be obtained from score charts in the coordinate system determined by the first two principal components. An animation can refine such information by highlighting data points by time or group. As in the gradient plots in the previous section, the advantage of an animated display is that there is no perceptual interference between the different subsets of data.

Figure 7 shows an animation of regional differences in the chemical composition of olive oil from different regions in Italy. The score charts draw attention to the fact that some groups of objects are more heterogeneous than others. By ordering the regions from south to north, or according to some characteristic of the areas, this type of animations can also highlight various gradients in the chemical composition.

Visual Detection of Change Points and Trends Using Animated Bubble Charts 337

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

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

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

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

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

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

memory.

et al., 2008).

direction.

highlighted at a rate determined by the user.

create a good overview of a complex dataset.

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