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bpierce

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Reply with quote  #1 
In his March 2008 Visual Business Intelligence article, Stephen Few wrote about the use of dual-scaled axes in graphs (for instance, a line graph that has a scale measured in dollars on its left side and a scale measured in units sold on its right side, with separate data corresponding to each). Stephen said that, originally, he accepted graphs with dual-scaled axes as a potentially useful solution. However, as time passed, he began to investigate dual-scaled axes more, and eventually came to the conclusion that they offer no unique benefits, but they do introduce several problems. In the article, Stephen said that he can think of no case where they are more effective than other methods, but he asked that people propose exceptions.

After reading the article, can you think of any cases that he did not address, where a graph with a dual-scaled axis would actually be the best solution?
silentd

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Reply with quote  #2 
I tend to agree with Stephen's assessment that graphs with dual-scaled axes are problematic.  In the few cases where I have attempted them, my audience found it difficult to discern which scale pertained to which data series. 

One possible approach for displaying the relationship between two sets of values is to calculate the ratio between the two.  To borrow an example from Stephen's article, if I want to show the relationship between revenue and units sold each quarter, one option is to calculate the quarterly revenue per unit sold, and graph the result as a single set of values.  This is by no means a silver bullet -- there are plenty of situations where showing the values separately makes sense -- but in some cases graphing the ratio helps to visualize how the two variables are related.

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David Katz
naomirobbins

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Reply with quote  #3 
I completely agree with Steve's position on the use of double-Y axes. However, I point out in Creating More Effective Graphs that is is often useful to use two scales for one axis when one is merely a conversion of the other. For example, one axis might show the temperature in Fahrenheit while the other shows it in Celsius.
sfew

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Reply with quote  #4 
Naomi,

Thanks for pointing this out. I should have mentioned this in the article. When two quantitative scales measure the same thing using different  systems of measurement, such as  U.S. dollars and  euros or feet and meters, it is meaningful and useful to place both scales on an axis (for example, on the Y-axis, with one on the left and the other on the right). What you're recommending is not a case of multiple data sets in a single graph that are measured along independent quantitative scales, which is what I've warned against in the article.

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Stephen Few
grasshopper

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Reply with quote  #5 
I agree it is usually confusing to have 2 y-axes when the data is plotted
with all-markers, or all-lines, or all-bars.

But I think it is sometimes useful to have 2 y-axes in the special case
where you have both bars & lines on the graph.


Also, I don't really like any of the examples I've seen so far that try
to overcome the 2-axis problem by converting the values to percentages.
They always make me wonder "percentage of what?", and greatly slow
down my interpretation of the graph.  Maybe I'm just "slow" that way...
wd

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Reply with quote  #6 
David (silentd) is on the right track.  Steve's second last pair of graphs (showing revenue and units sold one above the other) make it clear that revenues were somehow sustained even though units sold dropped. It begs the question of what happened to revenue per unit?  Rather than have the reader discover that fact and then try to work out some values, let's show it to them with a third graph of revenue per unit over time - all on one page of course.
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Bill Droogendyk
pstalker

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Reply with quote  #7 
I agree with silentd on the option of using different chart types with two axes.  Combining lines or dots with bars significantly reduces the risk of making invalid comparisons, while keeping the chart concise.
sfew

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Reply with quote  #8 
Peter (pstalker),

I don't think that silentd has proposed the use of different chart types with two axes. He suggested that when revenues are being compared to units sold through time, another way to display this relationship is as the ratio of units sold to revenue (that is, revenue divided by the number of units sold) in a single graph with a single Y-axis.

Regarding your suggestion, I sometimes combine lines or dots with bars in a single graph, but not with independent quantitative scales. I don't believe that the difference between bars and dots or bars and a line sufficiently discourages magnitude comparisons, which would not be appropriate if the scales are independent.

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Stephen Few
grasshopper

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Reply with quote  #9 
Good/useful bar-line overlays are difficult for me to come up with, but maybe a chart where the bars represent daily amusement park attendance (or daily icecream sales), and the line represents hourly temperature.

It might be useful to see them together, but they would also need 2 different scales (in particular, since the bar chart axis would need to start at zero, whereas the temperature line axis would not necessarily start at zero).

Of course, you could plot them as 2 separate plots, over/under each other, but the bar-line overlay could save space.

(I'm not a big fan of bar-line overlays ... just speaking from experience, a *lot* of customers ask for these though.)
sfew

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Reply with quote  #10 
Grasshopper,

I can't think of any reason why amusement park attendance and hourly temperature would be a more compelling candidate for a dual-scaled graph than any other. The comparison would be worthwhile, but in my opinion two graphs arranged one above the other provide a better solution. The confusion and opportunity to make meaningless magnitude comparisons in a dual-scaled graph is a big price to pay for a slight savings of space.

Of course, if the graph is for you alone and it works for you, there's no reason not to use it. It's when you're passing information on to others that problems arise.

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Stephen Few
bpierce

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Reply with quote  #11 
After reading Steve's article, Bob Gannon sent us an email to suggest a possible use for dual-scaled axes in graphs. His email and Steve's reply are included below:

Bob's Email

Stephen:

I always enjoy your Newsletter.  This month I would suggest an exception to your observations.

I think that a Line - Column chart that compares Net Income to Sales trends (plotting sales as a column against the left Y-Axis and Net Income as a Line against the right Y-Axis) can be a powerful analytical visual -- if you set the Scale on the right Y-Axis to be a target percent (e.g. 10%) of the left Y-Axis.

In the attached example, in addition to the trends in Net Income and Sales you can quickly see:

If Net Income is growing faster than Sales - a fundamental goal of any business, and

How close Return on Sales (ROS or Net Income/Sales) is to the goal - in the example 10%.

In the example the company is clearly growing Net Income faster than sales and reaches the 10% goal exactly in 2007.

Bob Gannon




Steve's Reply

Hi Bob,

Thanks for sharing this potential exception with me. As you’ll see, you set my mind to working. I understand what you’re trying to accomplish with your graph and agree that it works, but think that most people would find it confusing. For example, it took me a while to understand the significance of the positions of the data points along the line compared to the bars, even after reading your explanation. I think that this story could be told with less confusion if you use one graph for revenues and another immediately below it either for net income as a percentage of revenues compared to target or the variance of net income to target.

Here’s an example of the first approach:



Here's the second:



When you described your graph, you stated “the company is clearly growing net income faster than sales“, but we can't necessarily determine this based on the slope of the line alone (we have to perform mental math with the actual values). The slopes of the two lines cannot be accurately compared to determine relative rate of growth. In the example below, I have used a version of your graph to compare sales to net income, both of which are increasing at exactly the same rate of 10% per year. Notice that the slopes of the lines are not equal, even though the rate of change is equal.



Take care,

Steve


grasshopper

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Reply with quote  #12 
At first glance, my immediate visual perception is that I can
"see something" when I look at Bob's bar-line plot. 

But with Stephen's plots I don't immediately "see" anything.
It's too much work to look at them, and try to figure out
what's going on - a mental & visual chore :)

So, although Stephen's might be superior in a technical or
analytical sense, I prefer Bob's bar-line plot.
wd

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Reply with quote  #13 

To my mind, this display is really about Net Income as a Percent of Sales.  Steve made a graph like that.  Since we would simultaneously be interested in seeing the change in sales, I would consider putting a small vbar graph as an inset in the white space of Steve's line chart showing the annual sales dollars.


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Bill Droogendyk
grasshopper

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Reply with quote  #14 

Another example, and maybe food for thought & further discussion...

I came across another example of an overlaid bar/line plot that where it
seems useful to have a different left/right axis scale...  The line is the daily
temperature, and the bars are the rainfall (only for days that had rain).

Makes sense for the rain axis to start at zero and be plotted with a bar,
and for the temperature axis to only show the "plausible" range of
temperatures.  Of course the two graphs could be split out into 2 plots,
but I think they work pretty well overlaid in this case - although I'm
certain there will not be group concensus on this! :)


   http://robslink.com/SAS/democd25/pax.htm




nixnut

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Reply with quote  #15 
I don't see any added value in overlaying the two over separating them into their own graphs. Overlaying them cannot highlight a correlation since there doesn't seem to be one. So what happens instead is that they clutter each other making things harder to distinguish.
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