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neilism

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Reply with quote  #16 
This is an heroic effort to help us show data on a map, and there is a near primal urge amongst senior management to show things on the map!
 
Never really understood it, though. Most of the kinds of analysis I've been invovled in, including lots of geographical analysis, puts things in simpler buckets that are meaningful for the interpretation (e.g. number of householders between 18 and 24 within 5, 10, 15, 20 minute drive of proposed retail location). Mapping this information produces pretty pictures, but it's fiendishly difficult to explore. Roads, rivers, contours, forests -- all easily explored on a map, though... And some kinds of granular analysis are helpfully seen on a map -- e.g. where crimes with the same MO are being committed -- but these tend to be individual things plotted because their exact location is the thing that's important).
 
In the right setting, particularly where you don't have small, areas with high densities, I can see blocks being better than bubbles. But blocks are significantly worse at interpreting the information than the classic bars, etc.. The absolute position of the city/state/police station though familiar isn't relevant to most decisions as it's a category rather than a place in space. Possibly a feature of western, reductionist, command and control, patriarchal and heirarchical managment practices, though!
 
Eagerly anticipating circle being squared :-)
Francis

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Reply with quote  #17 
Since we are invited and challenged to build on the bricks proposal, I took a stab and created the concentric circles. (You can see the complete post on my blog, bu Stephen Few suggested that I post the proposal here to facilitate the discussion.)


It seems to me that the main issue with plain circles, the one that Few is addressing with bricks, is that they barely send a signal when they grow. A circle representing 8 units looks a lot like one representing 7 or 9 units.




Bricks on the other hand adopt a new shape, so it is very easy to see the difference.

 
Concentric circles do not go as far as bricks to show each unit, but they convey it more clearly than plain circles.

In the example above, each increase of one unit translates into one more concentric circle. Much like the plain circles, the concentric circles convey quantity by their size, adding to it the number of circles and the aspect of the outer rings. As the area grows in a linear fashion, the corresponding increase in radius diminishes and the circumference grows denser.

The advantage over bricks is that concentric circles can overlap and keep their identity.


Putting them on a map shows how their size and appearance combine to convey quantities. For instance, to my eye at least, California seems a little bigger than Arizona and, indeed, it is by 1 unit (click on map for real size). A clearer example would be Colorado and Wyoming, where the 1 unit difference is unmistakable.


Concentric circles have their downsides.

  • Above 5 circles, it is very difficult to count them. It is unlikely that a reader would rely on this method to compare quantities precisely.
  • The stroke can become problematic at greater sizes, when the difference between the circles is very small.
  • The visual is more complex than plain circles. This may create issues especially when interacting with certain backgrounds.
  • The distinction between sizes is less clear than bricks. Testing might tell us if it is any better than plain circles.

I have made some quick tests with variations in colors and full circles with white strokes. Neither seem to work as well as empty circles with colored strokes.




It might well be that this method is already well-known, although a quick search did not yield results. I’d welcome any pointer to anterior examples. It might also be that this method is adding less than it takes away. In any case, I thought I would add one more idea to this interesting discussion.

sfew

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Reply with quote  #18 
Francis,

Thanks for exploring the possibilities of concentric circles. Unfortunately, as you've seen, when there are more than three or four concentric circles, we cannot perceive the quantities by subitizing; we must attentively count them, which is very difficult to do because they are close to one another and hard to differentiate. Even with attention, it is very difficult to see the difference between a set of seven vs. a set of eight, and so on. Also, notice that sets of closely packed concentric circles beyond a small number create an annoying visual illusion of partially overlapping circles at the four cardinal positions (top, bottom, left, and right). You can see this especially in your map example. Even though this doesn't work, it was definitely worthwhile to make the attempt. Thanks for the contribution.

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Stephen Few
sfew

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Reply with quote  #19 
Pete,

Your observations and questions are insightful. People often display data on a map merely because they can, even though the location of values provides no insight. As you've shown through examples, many of the greatest insights from geospatially displayed data come from the details--individual values--but not all. To fully understand the stories that dwell in a set of data, we must examine it from many perspectives. This includes various levels of aggregation. For example, patterns that you might detect when viewing time-series values at the quarter or month level might be invisible when viewed at the daily level. Each level reveals useful information. Similarly, when viewing data geospatially, you can sometimes discover useful features at the state or country level that wouldn't be obvious at the level of each individual item or event.

It is because bricks are only useful when they display values that are aggregated to geographic levels that avoid overlapping that I've reassessed their worth. They are limited, but useful often enough to warrant consideration.

For someone with little experience with geospatial data displays, you're demonstrating a level of understanding that is extraordinary. Keep it up.

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Stephen Few
Francis

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Reply with quote  #20 
Thank you Stephen for your engagement -- it is much appreciated. Your comments and a suggestion received on Twitter encouraged me to explore the concentric circles further on my blog.

My goal is to improve on the circles to convey quantities on a map rather than to match or exceed the bricks, which I think do a fine job on the preattentive side. These were my challenges.
  • Get rid of the optical illusion.
  • Preserve the capacity to overlap.
  • Make the quantities easier to perceive.

Here are the concentric circles version 2.0.

The colors is now on the area instead of the stroke and there is a circular gridline every 5 units.

This design is less busy and does not create the optical illusion of version 1 at smaller sizes and lower resolutions.

The concentric circles can still overlap and preserve their shape.

And the circular gridline allows to see when certain thresholds are crossed on the circle, something that is not possible on a plain circle.

It is not possible to interpolate precisely between gridlines. Columns and bar charts suffer from a similar problem, but they hold two advantages. The first is that they generally have a gridline that exceeds the length of the longest column or bar.


The concentric circles 2.0 could do the same thing.


I don’t want to discard this solution entirely, but I am concerned that we will perceive the outer limit more than their colored area and overestimate the size of the circles. The cost seems to outweigh the benefit.

The second advantage of the bar is that the distance between the gridlines is constant. In a circle, it is well-known, the distance between the circumferences of concentric circles with areas of equal intervals gets smaller as they area grows. It is unlikely that people will adjust their perception of the distance and scale between each circular gridline.

I am not sure how much of a problem this is, considering that we are not aiming for the precision of a table, but rather for a visual method that allows a fair approximation. Still, the approximation is likely inferior to that of the column and bar charts.

The contribution of the concentric circles is that they make this confusing property of areas visible, while the plain circles do not.

Enough parading, time to put the concentric circles at work on a map. Click for real size.

Compare with the plain circles.

So, is it easier to visually estimate quantities with the concentric circles? The slight difference between Arizona and California seems more visible with the concentric circles, and easier to perceive than with version 1.0. The difference between Oklahoma and Louisiana, at least to my eye, is perceptible with the concentric circles, but barely with the plain circles.

Here are some other experiments that I discarded or keep for later versions.

 

The first one was inspired by a suggestion from Taimur Sajid on Twitter and it put me on the scent for the version 2.0 (thanks!). I find it too busy though and prone to the optical illusion and difficulties of counting rings. The gradient was too hard to test at different sizes (!). The other three are still too busy. There are still two options that hold potential however.


The shades replace or complement the circular gridlines. I ran out of time today to test them. I am concerned, however, that the shading will interfere with the transparency when circles overlap. Still, it could either reinforce the visual encoding for quantities, or simplify the design in the case of the one without strokes.

Finally, I used many of the default settings of my software. There’s more to try with different colors both for the area and for the strokes to make the concentric circles clearer. I look forward to the discussion, hoping to see more people weigh in because there is much to gain from a clearer depiction of quantities on a map or with areas in general.

danz

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Posts: 186
Reply with quote  #21 

Bricks
The good. They do perform better then bubbles when they do not overlapp, the available space is enough and amount of bricks is decent, for me 10 would be the limit.
Another good thing about bricks is that they aproximate in steps the values, a much easier way to group and compare. I think they just reassamble the same logic used for establishing the histogram bins. 
I also like the fact that the bricks can be used further across different dashboards or documents next to labels or within tables especially when data is sorted on different measures.
The bad. The values have to be associated with intervals in a linear ratio or logarithmic ratio, arbitrary ranges not being effective for bricks or bubbles. For such of situations different shapes and different color are the possible solutions.
The maps have to be redesigned to make sure the bricks do not overlap. That was discussed already.

Concentric circles
I like the way they handle the overlapping, but as Stephen said, is far more difficult to compare then bricks, especially above 3-4. However a possible improvement would be to mark the 5th, 8th and 10th circle either by using a more intense color or double the thickness.
On obvious downside is the ... size. For 10 levels and just one pixel space between level 9 and 10, makes 2 pixels difference in radius, which after some simple arithmetics makes minimum diameter of ~25 and a max of ~80 pixels (!), in case we want to keep the area of every circle in ratio with every level. In case we want to provide just an idea and do not use any area rule but a counting rule we still need a variation of diameter between 4 and 40. Of course, we can invoke the subpixel accuracy and high resolution devices, but still, it looks like a downside to me, obviously the bricks being much better from this point of view.

I am in the favor of using all possible enhancements to get the best out from any technique, but they have to be used only when they fits, not just because they exists. I think they worth to be implemented, but they just have to be carefully used by the analysts.

sfew

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Reply with quote  #22 
Francis,

Your experiments with concentric circles are interesting and it's clear that you're having fun exploring this, but the new version doesn't seem to work any better than the first, even though you've eliminated the one annoying illusion. We're still left trying to compare areas, and even though inner circles make this slightly easier, the comparison still requires too much effort and time. Also, to my eyes the patterns formed by the concentric circles are hard to look at--similar to targets on a gun range--which make me a bit dizzy. I appreciate your efforts to find a better solution, but I doubt that concentric circles will prove useful.

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Stephen Few
Francis

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Reply with quote  #23 
Stephen - Again, thank you for taking the time to react. I don't want to overstay my welcome or monopolize your discussion forum, especially if others want to comment on bricks or put forward their own solution, so I posted my last tweaks and conclusion on my blog. In short, I agree with the shortcomings that you identified, but the concentric circles still seem like a step up from the plain circles. Hopefully, someone will try to test them somewhere with real data and share their work.

Danz - Thanks for your feedback. I agree that the concentric circles are more difficult to compare than bricks. I have tried to highlight the fifth and tenth circle from version 1, but it came out busy (see above, with a black stroke on the fifth and tenth circles). And yes, with too many intervals, the space for the gridline becomes too small.
cpudney

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Reply with quote  #24 
G'day,

A very interesting article and subsequent discussion.

It lead me to wonder whether a slight variation in the arrangement of bricks would enhance the subitization effect.

The series below makes more marked changes in shape with each increment. It only alters elements 2, 4, 5 and 7. The idea is that by making the shapes more distinctive, recognition speed is increased. Whether this is true in reality would need to be tested.

Regards,
Chris.

Attached Images
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sfew

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Reply with quote  #25 
Chris,

While designing bricks, I played with several arrangements, including some that were similar to the arrangement that you've suggested. While your arrangement gives each quantity a unique shape, which is good, I think that the sequence isn't as intuitive as it is with the arrangement that I've proposed. In my arrangement, if a set of bricks is taller than another, it always means that it is greater in value. In your arrangement, a quantity of two is greater in height than a quantity of three, a quantity of five is greater than a quantity of six, and so on. I opted for an arrangement that grows in a consistent manner. It is certainly possible, however, that my arrangement is not the best. Different arrangements will need to be put to the test to determine what's optimal for recognition and comparison. I'm hoping that someone in a research group will tackle this questions and run some tests. If it turns out that your arrangement works best, I won't mind at all. Either way, I appreciate your efforts to improve the design of bricks.

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Stephen Few
cherdarchuk

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Posts: 29
Reply with quote  #26 
I have put together a number of maps featuring different marking options in this post. Francis's latest iteration of concentric circles are particularly effective when there is overlap.  They may not be as preattentively recognizable as bricks, but the extra contexts the rings provide is an improvement over plain circles. Perhaps they are solving a different problem than bricks were intended to solve, but I certainly wouldn't write off their usefulness.

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sfew

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Reply with quote  #27 
Since publishing my article about Bricks, I've learned about a similar construct that was proposed back in 1975 by a statistician named Robert Bachi. I learned this from Nick Cox, a statistician who teaches in the Department of Geography at Durham University in the UK. Nick is a rich resource for historical information about statistics. In a paper titled "Graphical Methods for Processing Statistical Data: Progress and Problems," published in the Proceedings of the International Symposium on Computer-Assisted Cartography in 1975, Bachi introduced a form of display called Graphical Rational Patterns (GRP). Below you can see a series of graphical objects that could be used to represent values 1-9 (i.e., individual units) and a second series that could be used to represent the values 10, 20, 30, etc. (i.e., tens). In the final example below, you can see how Bachi combined the two sets to display more precise values, in this case values 60-69. Bachi's method attempted to provide more precision than Bricks, but did so in a way that could not be fully perceived in a preattentive manner. The fact that he did not fully support preattentive perception is not surprising, however, given the fact that he published this work before much was known about this aspect of perception.

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Stephen Few

sfew

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Reply with quote  #28 
Cherdarchuk,

The concentric circles example is a bit misleading when paired with the Bricks example above it because it only shows a total of three quantitative intervals (three concentric circles), not nine as the Bricks do. Concentric circles beyond three intervals or so cannot be preattentively perceived. For this reason, concentric circles don't offer any real advantage over normal bubbles. When they consist of over three or four concentric circles, people will slow down and count the circles in order to compare the values, which is a slower process, though less precise, than comparing bubbles. You could actually achieve a better result be placing numbers of various sizes on a map, which could be read and compared more quickly and with greater accuracy than the concentric circles.

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Stephen Few
cherdarchuk

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Reply with quote  #29 
Stephen,

The example actually shows 10 different quantitative intervals, though only three levels are preattentively discernible.  The white ring in the bubble is like a tick mark on an axis. Concentric circles (which should probably be called marked bubbles or something else in their latest incarnation) are not as easy to discern as bricks, but are easier to compare than bubbles and they work well when overlapped. That ring makes it possible for me to see the difference between a bubble of size 6 and one of size seven, certainly not as easily as bricks, but much quicker and with more certainty than bubbles.  Your number theory was interesting, but it seems like it would only work if the numbers themselves were less than 10. Once multi-digit numbers begin overlapping it would get confusing. As I said before I don't think Francis's circles are a replacement for bricks, I think they are an improvement on bubbles.

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Name: numbers_o.png, Views: 106, Size: 18.28 KB


sfew

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Reply with quote  #30 
Chedarchuk,

It isn't obvious how the concentric circles (bubbles) should be read. The combination of differing circle sizes and ring sizes does not represent an intuitive or easily discernible sequence of values. Your example of encoding the values as text seem to confirm the point that I made: it is easier to compare the numbers than the concentric circles. Also, you could encode greater precision using the numbers. For example, imagine using a range of values from 1 to 9, with numbers only varying in size by intervals of 10 each. In other words, values from 80 through 89 would each have the same size and values from 90 through 99 would be slightly larger.

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Stephen Few
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