In the data below, there are two years of data for two different companies.

Here is all of the data plotted in a single chart.

Comparing data for a given company is most important, so I want to separate the data into separate charts for each company. But I still want to be able to compare the two companies. Here are my two charts.

Since Company 2′s data is higher, the maximum Y axis scale is larger. I could manually set the Y axis maximum for both charts to 120, but if the data changes, I’ll have to reset both charts again.

To determine what values to use, I add a small summary table near the main data table. Cells B10 and B11 compute the minimum and maximum of the data. Cells C10 and C11 show the values I will use. I want the minimum to be zero, so I simply type 0 in C10. I want the maximum to range with the data, so I enter =B11 into C11.

Copy C9:C11 and use Paste Special to add this data to each chart as a new series, with data in columns and series names in the first row (don’t worry about X values). Notice the two charts have the same Y axis maximum, because they have the same maximum value from the added series.

It’s a simple matter to format the added series to use no line, and the charts will magically stay in synch.

Te show the value of this approach instead of the manual approach, let’s add another year of data. Company 2 has really started to take off.

Here is all the data in one messy chart.

Here are the two original charts, with no attempt to synchronize axes.

Here is how the charts would look if the maximum had been manually fixed at 120. The 2012 data for Company 2 is cut off between Q3 and Q4.

However, if we make sure that our minimum and maximum formulas in B10 and B11 include the added data, the hidden series of both charts include the new maximum, so the axis scales are the same.

This is a very easy technique, applicable to line, column, and area charts (in all cases, change the added series to a line chart series). It can also be used for both X and Y scales of an XY chart if we determine minimum and maximum values for X and Y.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

A meaningful axis spacing allows a human viewer to make sense of the numbers in your chart.

Original Topsy Charts

Here is a chart of Twitter mentions of my blog over a one week period. Sorry the chart’s too wide, that’s as small as Topsy would make it and still have text large enough to read. You could right click on it and choose your browser’s equivalent of “Open Image In New Tab” to see it in all its glory.

Here’s the Topsy graph for two weeks.

Notice anything wrong with these charts? No, they do have the right number of points. But the vertical gridlines and the horizontal axis labels are not aligned with the points. In the 7-day chart (top), there are 8 labels between the axis min and max values. To accommodate this mismatch, some adjacent pairs of tick marks fall within the same day, so a couple of labels are repeated. In the 14-day chart (above), there are 9 labels between the axis min and max value; some days have no tick marks, so dates are left out, but not in a regular pattern.

This kind of unorthodox labeling causes the humans to have to think too much about the chart. Sometimes the choice of incredible charting options like this leads to lack of credibility of the whole chart.

Human-Friendly Axis Spacing

In a 7-day graph, what would be an intuitive axis tick spacing? Let’s try one day, since one week is too wide and one hour too narrow. In general, numbers that are 1, 2, or 5 times a power of ten make good values for axis tick spacing. 1, 20, 500, 0.01, and 0.5 are reasonable choices. If the scale is days, and a spacing of 1 or 2 days result in crowded labels, 7 days is a reasonable choice.

Here I’ve reconstructed Topsy’s 7-day chart with a 1-day axis tick spacing. It’s very natural, the ticks and gridlines are spaced the same as the data points, one day apart. Nobody has to use any excess gray matter to understand the time scale.

Here is the 14-day Topsy data plotted with a 1-day axis spacing. It is as easy to read as me 7-day chart with 1-day spacing, which is to say, much easier than the Topsy Turvy spacing in the original chart.

This is really more axis labels than are needed, and some of them are forced to wrap so they don’t overlap. We can fix this by using a 2-day axis spacing. Also easy to read. I’ve helped the viewer by placing small minor tick marks at 1-day intervals.

Intermediate gridlines work as well as intermediate tick marks.

Topsy’s Axis Scale Parameters

So what was Topsy thinking? Well, I can’t answer that, but I can estimate the axis tick positioning that they used.

Here is Topsy’s 7-day data. I’ve secretly replaced the regular time scale axis with an XY series that has spacing independent of the actual plotted points. Vertical error bars on the invisible points serve as my gridlines. The X values are based on formulas I can tweak in the worksheet, and I align the custom gridlines to closely resemble the original Topsy alignment. Jan 13 and Jan 15 both appear twice as in the original chart.

To get the spacing right, the first gridline appears at 3:44 pm on January 12, which rounds up to the Jan 13 shown in the label. Each subsequent gridline is 16 hours and 40 minutes after the previous one. I think we can all agree that 16:40:00 is not as intuitive as 24:00:00.

I’ve reproduced the 14-day chart as well. The first gridline appears at 3:20 pm on January 5, which rounds up to Jan 6. Subsequent labels are 33 hours and 20 minutes apart. Again, not so intuitive.

I can’t really say where these strange tick spacing values came from, but I have a suspicion. 16:40 is 1000 minutes, and 33:20 is 2000 minutes. If the time dimension were plotted in minutes, the two charts have ranges of 8640 minutes (7 days) and 18720 minutes (14 days), so in fact 1000 and 2000 are human-friendly numbers. Of course, the data is spaced 1440 minutes apart, so the nice minute-based axis spacing is really irrelevant.

I suspect the charting mechanism has a nice algorithm to calculate the spacing based on the minimum and maximum data values, but it doesn’t consider the actual data spacing, nor does it investigate alternative units. And the algorithm was automated before a human had a chance to look at it and say “Huh??”

My current Klout ranking?

I dunno, I guess that’s pretty good. Some of my colleagues, and the people I follow on Twitter mostly fall in the range between 25 and 55. So who else has a 43? My fellow Excel chart master, Jorge Camoes, has a 43. An old college buddy, Joel Foner, has a 43. So does fellow Microsoft Excel MVP Ken Puls. Annmariastat has a 43, and she doesn’t even have a Klout account, but she has a Wikipedia entry. So I’m in good company.

There’s some kind of algorithm that determines this score, based on how many people I influence through my internet presence (I guess, how many people follow me), how much I influence them (how often they repeat what I say), and how influential the people I influence are.

The first thing I noticed when I followed the link in the email this morning (I delete most Klout emails without following the link) was this chart showing my score over the past month.

Wow, a few days ago, I really got a huge boost in my score.

Then I looked a little more closely, and read the axis labels. Over the past month, my score has ranged from about 42 to about 43.

This is a good example of how the scale of a value axis can exaggerate or play down the variability in a signal. Here I’ve reproduced the Klout timeline in Excel:

The total variation in the displayed data is about ±1.8% from the mean. It looks ginormous when the visible Y axis scale is less than 5% of the maximum value. It doesn’t look so substantial when the Y axis scale starts at zero:

Maybe there’s a reasonable intermediate scale. This scale shows some variation, but it doesn’t look like a tsunami:

Another funny thing about Klout is the listing of topics that I’m influential about. Data Visualization is rated Strong, and Visualization is rated High. Well, that’s good, those are topics I’d like to think I’m influential about. New England is rated High? Well, in season I will occasionally tweet about the Red Sox, but that’s the extent of my internet discussion about my home region. Statistics, Technology, good to see both of these here.

But further down the list. Disease? Why am I listed for Disease? Sure, I’m a doctor, but not of medicine. As Randy Pausch‘s mother said of him, “He’s a doctor, but not the kind that helps people.”

Jorge Camoes (who also has a Klout score of 43) says Klout must think I’m sick (insert a pun here for influence/influenza). Klout tells Jorge that he is influential for Coffee, from which he abstains in real life.

Microsoft Excel falls far down my list of topics. Not lowest, but as far as the screen shot could capture. Why am I only Medium for Excel? I’m a Microsoft MVP for Excel, and Excel is one thing I talk a lot about.

I guess this Topics of Influence algorithm needs a bit of work.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

The Problem

People frequently ask how to show vastly different values in a single chart. Usually they ask because a few very large values (for instance, Paris in June or Madrid in May in the chart below) overwhelm the other, relatively much smaller, values.

Logarithmic Scale

One suggestion is to use a logarithmic scale. For scientific data presented to scientific audiences, this is often an excellent suggestion. For the general public, and for general data, this may not be so useful. Especially in a bar chart, where the length of bars is important to comprehension, not some mathematical abstraction of length.

Broken Axis

Another suggestion is to “break” the axis, so that part of the axis shows the small values, then another part of the axis shows the large values, with a section of the axis scale removed. Sounds good, but you’ve lost any correlation between the large and small values. Also our eyes are likely to see the two broken bars in the chart below as only about twice the value of the tallest of the unbroken values (despite our conscious brains “knowing” that the axis has been cut).

Another problem with this approach is that it’s cumbersome to create and nearly impossible to maintain charts like this.

Panel Chart

A better suggestion than either a log scale or a broken axis is to plot the data in a panel chart. This chart has two panels, one with an axis that shows all the data, the other with an axis that focuses on the small values. I generally advise strongly against using any kind of gradient in a chart, because the gradients are pretty much meaningless. In this chart, the gradient at the tops of the (truncated) large values are not meaningless, but are intended to show the large values extending high up into the clouds.

Making the Panel Chart (It’s Easy!)

If you want to play along at home, the data is located in BrokenYData.csv.

The panel chart is really not too complicated. It consists of one set of data plotted on the primary axis and another set on the secondary axis. The primary axis data shows all the data using the full Y axis scale.

The secondary axis is scaled to show the smaller values. Note that the two very large values (>30M) have been truncated at a suitably small value (7.5M).

When seen as part of a panel chart, the primary axis (left of chart) has been scaled so that its data occupies the top half of the chart.

The secondary axis (right) has been scaled to keep its data within the bottom half of the chart.

It only takes a little experience, imagination, and knowledge of algebra to choose suitable scales. Fortunately readers of my blog are gifted in these characteristics.

The first step in creating this panel chart is to plot all six series (primary and secondary versions of the original three series).

One by one, format the last three series to move them to the secondary axis. Then rescale the two axes as shown above, to allocate the primary and secondary to separate panels.

Format the secondary series so they have the same fill colors as the corresponding primary series.

Clean up the axis labels using custom number formats: [>=0]0,,"M";;; for the primary axis and [<8000000]0,,"M";;; for the secondary axis. Remove the redundant legend entries: click once on the legend, then again on the duplicate label, and press Delete.

As I mentioned, use of gradient fills is usually useless or even harmful formatting. However, I’ve formatted the truncated bars in the bottom panel of this chart to (try to) indicate that they extend higher than their neighbors, into the clouds. Here are the settings I used. First I selected just the one data point (bar) by single clicking on it twice. The first click selects the whole series, the second selects just the one point. I chose a gradient direction that puts the light end of the bar at the top. I moved the middle gradient stop to 80%, so the gradient is confined to the very top of the bar. I set the bottom and middle gradient colors to the fill color of the series, and I set the top gradient color to white.

Here is the finished panel chart, repeated here for your viewing pleasure.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

Comparison of Line Charts and XY Charts

Essentially, the difference is that Line charts plot X values as nonnumerical categorical values, like {A, B, C}; XY charts treat X values as continuously varying numerical values. Here is a brief comparison of the two chart types:

A Typical Line Chart

A user is simply trying to create an XY scatter plot in Excel where the X axis values as shown in the example below can be maintained as-is on the final graph’s X axis points:

This data is perfectly suited for a line chart.

When you try to use the data in an XY chart, Excel ignores the non-numerical X values, and substitutes counting numbers, 1 for the first category, 2 for the second, etc.

For some reason, the user is insisting that a scatter plot is used, and all they want is the X axis to end up exactly as the line graph is formatted. I suspect this is due to a lack of understanding of the axis differences above, but I’ll never know, because this user is someone else’s client.

Making an XY Chart Mimic a Line Chart

An XY chart can be used to display this data, but it is a poor second choice. The tricks that are needed to make an XY chart display the nonnumeric labels like a line chart make the fake labels static, and they must be rebuilt if the amount of data expands, or if rows are inserted or deleted.

But I understand users, so here is the second option, which is what he thinks he wants, not what he needs.

We need to adjust the data. Since the Line chart X values are unsuited for an XY chart, we must insert a column of valid X values. To accommodate the Line chart style axis labels, we will use a dummy XY series along the X axis, which serves as placeholders for data labels which will look like the Line chart labels. The dummy series uses the column of zeros.

Select the yellow shaded range, and make an XY chart.

Hide the standard X axis labels but maintain the margin beneath the axis by using custom number format of ” ” (space character). If you simply format the axis with no labels, the plot area will be too close to the bottom of the chart, without leaving room for the dummy labels.

Use Rob Bovey’s Chart Labeler (a free utility that is indispensable for creating and manipulating custom labels) to label the dummy series. Apply the labels in the first column of the data (not shaded yellow in my example) to the “Label” series.

Each label remains linked to its cell. If the chart stays at 4 points using the same range, the labels will update as these cells are changed. Stretching the range or inserting/deleting rows will force you to rebuild the axis.

Finally hide the “Label” series by formatting it without markers or lines.

That’s a long way to go to mimic a completely dynamic Line chart with an XY chart which may need subsequent maintenance if the data changes. The wrong wrench, as we say, to hammer in the wrong screw.

Peltier Tech Update

Last week I had the pleasure of attending the Juice Analytics Viva Visualization tour at the Juice Boston Tea Party. They served breakfast, then presented their take on data visualization. Basically, they remind us to send a message, keep the visualization simple, put it in context, and follow good design fundamentals. We’ve heard the message many times before, but it’s worth retelling, especially by these experts who build solutions for big clients. Among the takeaways are:

• Don’t let novelty obscure the data.
• Don’t let visuals obscure the data.
• Choose the right chart type.

There is a lot of great content on the Juice web site and blog, including a guide for choosing the right chart.

The Learning As You Go blog has a nice article about plotting highly skewed data, at Graphing Highly Skewed Data. The article covers use of secondary axes (a bad idea), breaks in the axis (also a bad idea), logarithmic axis scales (okay if users understand log scales), and multiple charts. This article is a response to a discussion started by Chandoo in How do you make charts when you have lots of small values but few extremely large values?

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
 

I have been asked this question a number of times, and being a founding member of Chart Busters, of course I know the answer. I’ve answered the question a number of times, but if I answer it here, it will become available for the ages.

I describe the problem and how to correct it. If you are really interested, I finish with an explanation of why this happens.

The Problem

Let’s use some very simple data to illustrate the problem.

Let’s make a simple bar chart.

The labels were sorted from top down in the worksheet, but they appear from bottom up along the chart axis.

The Fix

It’s easy, if tedious, to correct the order of category axis labels. Select the axis, press Ctrl+1 (numeral one), the universal shortcut in Excel for Format This Object, and in Excel 2003 the following dialog appears.

The fix is simple: check the two boxes for Categories in reverse order and Value (Y) axis crosses at maximum category.

The protocol in Excel 2007 is the same, except the dialog looks a little different. You select the same options, but they are located far apart on the dialog.

This changes the order of axis labels in our bar chart.

If you forget to make the value axis cross at the maximum category, the axis will now appear at the top of the chart. After reversing the order of the categories, the maximum category is at the bottom of the axis.

Why Does Excel Do That, Anyway?

If we use the same data to make a column chart (line and area chart, too), the labels go from left to right, as expected.

Take another look at the column chart, and note where the origin of the axis system is located. I’ve indicated the origin with a red circle.

The values start low (at zero in this case) at the origin and increase in value as they move away from the origin. The category labels start with the first one next to the origin and later labels in the list extend further from the origin.

Now look at the bar chart and consider the origin of its axis system.

The values start low (zero) at the origin and increase in value as they move away from the origin. The category labels start with the first one next to the origin and later labels in the list extend further from the origin. Just like in the column chart.

Perhaps this is better illustrated if we remove the category data from the bar chart. In this case, Excel uses the counting numbers 1, 2, 3, etc. in place of the empty categories.

Both axes have low numbers next to the origin and higher numbers further away.

The whole problem arises because Excel follows the same axis ordering scheme for bar chart category axes as for any other axis in any other chart.

This describes the mechanics of axis label ordering. But, 99% of the time, a user expects the axis labels to go in the same order top to bottom as in the data source. Why Are My Excel Bar Chart Categories Backwards? is still a valid question: Why can’t bar chart categories automatically be reversed? Alternatively, why can’t the options for a bar chart’s category axis default to:

Works for me.

Peltier Technical Services, Inc., Copyright © 2011.
 
Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.