# Quantitative Displays for Combining Time-Series and Part-to-Whole Relationships

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1 Quantitative Displays for Combining Time-Series and Part-to-Whole Relationships Stephen Few, Perceptual Edge Visual Business Intelligence Newsletter January, February, and March 211 Graphical displays of quantitative information always feature particular relationships among the values. Two of the most common are time-series and part-to-whole relationships. In the former case we feature how values change through time, and in the latter how values that combine to form a whole compare to one another and the whole (for example, a regional breakdown of total sales). Determining the type of graph to use and its design should be based primarily on the nature of the one or more relationships that it features. For example, when we want to show how values change through time (a time-series relationship) in a way that makes the trends and other patterns easy to see, a line graph is often the best solution. In this article, I will propose graphical solutions for those occasions when we must feature a combination of time-series and part-to-whole relationships that is, how the relationships among the parts of some whole change through time. Traditional Graph Solutions Combined time-series and part-to-whole relationships are typically displayed using one of the following graphical solutions: A series of pie charts A series of stacked bars A stacked area chart Let s take a look at each and evaluate their strengths and weaknesses. In each case, we ll use the following series of twelve monthly sales values (the time-series relationship) divided across four geographical regions (the part-to-whole relationship). Pie Chart Solutions Here s how this story could be told using pie charts: Copyright 211 Stephen Few, Perceptual Edge Page 1 of 1

2 One of the first things you might have noticed is the fact that, while the slices of each pie show the regional percentages of sales, total monthly sales aren t displayed at all. One way to add this information to the display is to vary the sizes of the pies, which I ve done in the following example. If we were to list the benefits of this particular solution, the list would remain empty. This solution fails in every respect. A single pie chart already fails as a way to compare parts of the whole easily and accurately. Visual perception simply isn t tuned to compare the sizes or angles of the slices, except in a very rough sense. Multiplying the number of pie charts magnifies the failure by making it virtually impossible to see how the regional sales values changed through time. Try it for yourself. See if you can explain how regional sales went up and down through time and how the relationship between the regions changed through time. As you can see, this is not a viable solution. Stacked Bar Solutions Here s a stacked bar chart that displays the same information: 4, 35, 3, 25, 2, 15, 5, Just as it s difficult to compare the slices of a pie, it is difficult to compare the segments of a stacked bar. If the segments were arranged side-by-side and all grew upwards from the same baseline, it would be easy to compare their heights, but when stacked upon one another, the task becomes hard. Plus, although it s fairly easy to see how total sales changed from month to month and how sales in the region changed from month to month (the blue segments of the bars at the bottom, which share a common baseline), it is quite difficult to see how sales in the other regions changed. Difficult, but still a bit easier to do this using stacked bars rather than pie charts. Bars don t do a good job of showing overall trends and other patterns of change through time. Lines do this much better. If you re tempted to believe that this problem can be solved by adding lines to connect the tops of each segment across the entire set of bars, take a look at the following example and determine for yourself if this helps. Copyright 211 Stephen Few, Perceptual Edge Page 2 of 1

3 4, 35, 3, 25, 2, 15, 5, One of the immediate problems you ll notice is that this looks quite cluttered, even though I ve kept the design clean and simple. Beyond this, the bigger problem is the fact that you cannot use the lines to follow the pattern of change in regional sales, except for the bottom segment (the region in blue in this case). Other than this one exception, the lines can only be used to ever so slightly assist in determining the amount of change from one bar to the next not by following the slopes of the lines up or down, but by examining the difference between the vertical distance from the lower to the upper line where they connect to the bar on the left versus where they connect to the bar on the right. The slight assistance that the lines provide does not overcome the problem caused by the clutter or our tendency to focus on the slopes of the lines. Because bars are so visually weighty and separate from one another, they do a good job of focusing our attention on one month at a time. In situations when patterns of change aren t part of the story that you re trying to tell and you instead want to focus attention on sales in particular months, one at a time, or to compare one particular month to another, a stacked bar chart will do the job. Otherwise, better solutions are available. Stacked Area Solutions Here s the same data in a stacked area chart: 4, 35, 3, 25, 2, 15, 5, Copyright 211 Stephen Few, Perceptual Edge Page 3 of 1

5 Solutions with Few Parts For this situation, I usually recommend the following solution: US \$ 21 Sales 4, Total 35, 3, 25, 2, 15, 5, 2, 18, 16, 14, 12, 8, 6, 4, 2, Consider the attributes of this approach: 1. The trend and patterns of change in total sales are readily available to our eyes. We can focus on total sales without being distracted by the regions. 2. The trend and patterns of change in regional sales are easy to see and compare. 3. The contributions of the parts are easy to see and compare at any point in time. 4. Because specific points in time in the two graphs are aligned, you can easily see the total sales at a particular point in time in relation to regional parts that make up that total. 5. The trend and patterns of change in total sales are easy to compare to the trend and patterns of change in any of the regions. Copyright 211 Stephen Few, Perceptual Edge Page 5 of 1

6 Although there are occasions when slight variations of this solution might work as well or better (for example, replacing the line graph for the whole with a stacked area chart), this simple solution seems to work well most of the time. A variation that s sometimes useful adds a third graph that expresses the contributions of the parts as percentages of the whole, illustrated below. 21 Sales \$4, Total \$35, \$3, \$25, \$2, \$15, \$ \$5, \$ \$2, \$18, \$16, \$14, \$12, \$ \$8, \$6, \$4, \$2, \$ 5% 45% 4% 35% 3% 25% 2% 15% 1% 5% % Copyright 211 Stephen Few, Perceptual Edge Page 6 of 1

7 You might wonder if it would ever make sense to place the values of the whole and the parts in a single graph rather than two. Here s what this would look like using the same data: US \$ 4, 21 Sales Total 35, 3, 25, 2, 15, 5, In this particular case, because there are only four parts, values of the whole are not so much greater than values of the parts that they can t effectively be displayed in a single graph. In many cases, however, placing the whole and its parts in a single graph would force the lines representing the parts into a narrow range at the bottom of the scale, which would flatten the lines to such a degree it would be difficult to see and compare their patterns of change. Solutions with Many Parts As you can imagine, the solution that I proposed above would decline in effectiveness as the number of parts increased, due in part to clutter. This same solution could continue to work when there are many parts, however, if we enhanced it in one of two following ways: By allowing specific parts to be highlighted interactively to feature them By placing each of the parts or smaller groups of parts into separate graphs If the software that you re using to display data supports selective highlighting of lines in a line graph, even though the graph is cluttered with many lines, this problem can be reduced by highlighting particular lines when you want to focus on them, thus removing distraction caused by the others. In the following example, 13 products are displayed in the bottom graph, but only two have been highlighted, which makes it easy to compare them with little distraction from the other products: Copyright 211 Stephen Few, Perceptual Edge Page 7 of 1

8 In this example, created using Tableau Software, I highlighted two products in the lower graph Chamomile and Green Tea by selecting them in the legend to the right of the graph. Other interactions can be enabled as well for a richer analytical experience, such as filters using the controls that appear in the upper right. Copyright 211 Stephen Few, Perceptual Edge Page 8 of 1

9 If you re stuck with a static view with no opportunity to highlight particular lines, you can solve the clutter problem by breaking the parts into multiple graphs, as illustrated below. When you use this approach, it s important that you group the parts in a meaningful way. In this example, it was easy, because these beverage products could be divided into two manageable groups based on the natural groupings of coffees versus teas. It isn t always this easy. If no natural way to break the parts into groups can be found based on a categorical dimension, it might make sense to break them into groups based on quantitative ranges. For example, using the products in the example above, they could be divided into two graphs one with revenues up to the 15% range and the other for everything higher or perhaps into three groups ranging from (1) to 1%, (2) over 1% to 2%, and (3) over 2%. For frequent graphical display requirements, such as combined time-series and part-to-whole relationships, it helps to have a few proven solutions at hand and to understand the strengths and limitations of each. Reserve the mentally taxing work of creating a new solution for those occasions when the requirements are genuinely novel. Copyright 211 Stephen Few, Perceptual Edge Page 9 of 1

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