Graphing Levels and Rates

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Dan Goldner dan ventanasystems.c
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Graphing Levels and Rates

Post by Dan Goldner dan ventanasystems.c »

Posted by Dan Goldner <dan@ventanasystems.com>
It is well established that most people cannot easily perceive the relationships among an inflow, an outflow, and a stock by looking at their time series. Thus, exercises in graphical integration (e.g. Sterman, Business Dynamics, chapter 7.1.3) are an important part of SD training.

I am on a quest for a graph that not only allows quantitative comparison of levels and rates, but also makes the causality immediately obvious, even to an untrained viewer. Traditional approaches simply superpose the three time series:

http://www.ventanasystemsinc.com/private/dan/tradit.jpg

While this does show the size of the rates (over an interval) compared to the level, it falls short because the viewer must still mentally ""carry"" the net inflow up and add it to the total.

I've made three attempts to combine inflow, outflow, and stock time series in a single design that shows what is happening. My first attempt:

http://www.ventanasystemsinc.com/privat ... tempt1.jpg

highlights turnover or churn, but with the drawback of spatially separating inflow and outflow so they cannot be easily compared to one another. The second attempt:

http://www.ventanasystemsinc.com/privat ... tempt2.jpg

uses sloped whiskers to indicate what the total would have been at each point, if there were only an inflow (top whiskers), or only an outflow (bottom whiskers). While this version properly indicates all time rates of change by slopes, and makes them comparable to each other as well as to the level, it is creepily insect-like. It is also redundant: once two of the inflow, outflow, and level are graphed, the third is implied. The last attempt:

http://www.ventanasystemsinc.com/privat ... tempt3.jpg

removes that redundancy by plotting just the level and the outflow. The inflow is indicated by the vertical distance from the end of the whisker to the point above it, and 'remaining' is separated from 'new' by the ends of the whiskers. This is my favorite so far, but it is quite different from familiar graphs, and I am stumped for the clever legend, caption or other annotation required to explain it to the untutored viewer.

The above can be improved, or perhaps there is a better, completely different approach. I posted this question to Edward Tufte's forum on information design (http://www.edwardtufte.com/bboard/q-and ... _id=0000yO
-- scroll down to November 14, 2005)

but received few responses. It did make me the number 1 hit, if only for now, of Google searches for ""sloped whiskers"".

Can some wise reader of this list advance the cause?

Many thanks,

Dan Goldner

Posted by Dan Goldner <dan@ventanasystems.com>
posting date Mon, 21 Nov 2005 17:30:35 -0800
Tom Fiddaman tom ventanasystems.
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Posts: 2
Joined: Fri Mar 29, 2002 3:39 am

Graphing Levels and Rates

Post by Tom Fiddaman tom ventanasystems. »

Posted by Tom Fiddaman <tom@ventanasystems.com>
Personally I like:

> The second attempt:
>
> http://www.ventanasystemsinc.com/privat ... tempt2.jpg
>


People are used to fishbone diagrams so I don't see a problem with creepiness. My immediate reaction was to interpret the diagram as a bunch of strings, with the whiskers as tension pulling the central level line up or down. It might work to present this as a particle (or insect) responding to forces as it moves through time.

I think the redundancy is helpful because the inflow and outflow may be interesting in their own right. I suspect that graphical integration is intrinsically mentally challenging, so any simpler plot that shows 2 of 3 series becomes a hassle for the user - ink is cheaper than neurons. The stock probably can't be omitted because the user then has no way to know it's initial value.


This graph even permits extensions; for example, multiple inflows and outflows could be shown at once (with different colors or endpoint
markers) as long as their values didn't coincide too much. The flows shown need not be consistently in or out; they could cross the level line.

If there's any problem with this approach it's that the discrete whiskers emphasize discrete time thinking. It reminds me of the typical presentation of a discrete random walk. In the limit as dt->0, the whiskers become vertical and pack together to become a shaded area, so a similar graphic could work for continuous output, though I suspect the meaning of a shaded area would be less clear to a viewer.

It's interesting that the Tufte crowd didn't take the bait. A pointer to something like Sterman's Cloudy Skies experiment with some hints about the challenges of mental integration might help; it would be interesting to see approaches from other paradigms.

Tom


****************************************************
Tom Fiddaman
Ventana Systems, Inc. http://www.vensim.com
1070 Bridger Woods Rd Tel (406) 582 4911
Bozeman MT 59715 Fax (202) 315 3570
Tom@Vensim.com http://www.sd3.info
****************************************************
Posted by Tom Fiddaman <tom@ventanasystems.com>
posting date Tue, 22 Nov 2005 11:22:48 -0700
Sean Morgan Morgan JantzMorgan.c
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Posts: 1
Joined: Fri Mar 29, 2002 3:39 am

Graphing Levels and Rates

Post by Sean Morgan Morgan JantzMorgan.c »

Posted by Sean Morgan <Morgan@JantzMorgan.com>
I found the second attempt (whiskers) more intuitive and thought provoking than the others. Attempt 3 with only one set of whiskers again made me do visual math...so having all the bits on the page was nice. You might also do something with color. ....e.g. high flow rates have darker shaded lines and inflows could be a different color from outflows. Coordinating the colors with the causal loop diagram would help make the link.

________________________________________

Sean Morgan
President
Jantz Morgan LLC
Quantitative Investment Management
www.jantzmorgan.com
Posted by Sean Morgan <Morgan@JantzMorgan.com>
posting date Tue, 22 Nov 2005 15:17:11 -0500
rgd6 cornell.edu
Junior Member
Posts: 9
Joined: Fri Mar 29, 2002 3:39 am

Graphing Levels and Rates

Post by rgd6 cornell.edu »

Posted by <rgd6@cornell.edu>
I agree with Tom. The attempt2 is by far the most intuitive, at least for
me. Nothing wrong with fish bones or insects! I find the tradit my second
favorite.

Attempt2 also gives an intuitive feel for the role of the delta t.


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Posted by <rgd6@cornell.edu>
posting date Thu, 24 Nov 2005 00:21:07 +0700
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