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	<title>Comments on: Tax the Rich, or Deceptive Axis Scales</title>
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	<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/</link>
	<description>Peltier Tech Excel Charts and Programming Blog</description>
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		<title>By: Lying with Charts, and How to Find the True</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-27007</link>
		<dc:creator>Lying with Charts, and How to Find the True</dc:creator>
		<pubDate>Mon, 15 Feb 2010 17:51:09 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-27007</guid>
		<description>[...] writes about the flaws in both charts, so I’m not going to discuss them [...]</description>
		<content:encoded><![CDATA[<p>[...] writes about the flaws in both charts, so I’m not going to discuss them [...]</p>
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		<title>By: Weltanschauung, Lies and Charts</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-17951</link>
		<dc:creator>Weltanschauung, Lies and Charts</dc:creator>
		<pubDate>Wed, 19 Aug 2009 20:54:27 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-17951</guid>
		<description>[...] writes about the flaws in both charts, so I’m not going to discuss them [...]</description>
		<content:encoded><![CDATA[<p>[...] writes about the flaws in both charts, so I’m not going to discuss them [...]</p>
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		<title>By: Jon Peltier</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-17563</link>
		<dc:creator>Jon Peltier</dc:creator>
		<pubDate>Tue, 11 Aug 2009 12:22:38 +0000</pubDate>
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		<description>Matt -

I think the overriding factor is that cognitively our visual perception tells us the bars are showing length, because the bars start and end somewhere. Even &quot;knowing&quot; that it&#039;s the top endpoints of the bars that encodes the values does not overcome what we see, which are the top and bottom endpoints of the bars, and the bars themselves between these endpoints.</description>
		<content:encoded><![CDATA[<p>Matt -</p>
<p>I think the overriding factor is that cognitively our visual perception tells us the bars are showing length, because the bars start and end somewhere. Even &#8220;knowing&#8221; that it&#8217;s the top endpoints of the bars that encodes the values does not overcome what we see, which are the top and bottom endpoints of the bars, and the bars themselves between these endpoints.</p>
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		<title>By: Matt Cloves</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-17560</link>
		<dc:creator>Matt Cloves</dc:creator>
		<pubDate>Tue, 11 Aug 2009 11:52:29 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-17560</guid>
		<description>Jon,

Firstly, great site, please keep up the good work.
I really am very grateful for the time you put into passing on your insights.

I think this distinction between values encoded by their position, and values encoded by their length, is interesting.

(coming at this from a largely lay-person perspective)
While I appreciate that the presence of a &#039;bar&#039; below the &#039;top line&#039; of a bar in a bar chart could have assumed, or subconcious/implied(?) meaning, if we can assume that we are not using a stacked bar chart, and that all the points start on the same level, are we not effectivley looking at the &#039;top line&#039; and its relative potision to other &#039;top lines&#039;? A kind of disconnected line chart. (ie. points encoded by their position)

Now, i&#039;ll admit that if we were to lop off the bottom of a bar chart, and start some way up the axis, you would lose the ability to quickly gauge the changes between years (in this case), as they relate to each years totals (ie. did that loss of 3 represent a reduction of ~5%, or ~50%).
but do you not suffer the same loss in a line chart?

does this come down to one better method (bar) for comparing any year to any other, and one better method (line) for the trend over many years?
or is there some other aspect that is lost when you start a bar chart from half way, that isn&#039;t such a factor with line charts.</description>
		<content:encoded><![CDATA[<p>Jon,</p>
<p>Firstly, great site, please keep up the good work.<br />
I really am very grateful for the time you put into passing on your insights.</p>
<p>I think this distinction between values encoded by their position, and values encoded by their length, is interesting.</p>
<p>(coming at this from a largely lay-person perspective)<br />
While I appreciate that the presence of a &#8216;bar&#8217; below the &#8216;top line&#8217; of a bar in a bar chart could have assumed, or subconcious/implied(?) meaning, if we can assume that we are not using a stacked bar chart, and that all the points start on the same level, are we not effectivley looking at the &#8216;top line&#8217; and its relative potision to other &#8216;top lines&#8217;? A kind of disconnected line chart. (ie. points encoded by their position)</p>
<p>Now, i&#8217;ll admit that if we were to lop off the bottom of a bar chart, and start some way up the axis, you would lose the ability to quickly gauge the changes between years (in this case), as they relate to each years totals (ie. did that loss of 3 represent a reduction of ~5%, or ~50%).<br />
but do you not suffer the same loss in a line chart?</p>
<p>does this come down to one better method (bar) for comparing any year to any other, and one better method (line) for the trend over many years?<br />
or is there some other aspect that is lost when you start a bar chart from half way, that isn&#8217;t such a factor with line charts.</p>
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		<title>By: Krish Swamy</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-16736</link>
		<dc:creator>Krish Swamy</dc:creator>
		<pubDate>Sun, 26 Jul 2009 12:00:36 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-16736</guid>
		<description>Great display of how putting a Min on the y-axis or setting a Max of 100% on the x-axis can give a misleading picture. It leads me to wonder what would have been right ways of showing this information. 

Btw, I am not sure a line-graph does not produce the same misinterpretation. In several circles, line graphs, bar graphs and area plots are used interchangeably. People don&#039;t necessarily pay attention to the fact that line graphs should be used mainly to depict time-series. 

One possible Min could be the minimum tax rate in industrialized countries. It could be the min-rate in top 30 industrialized nations or the top 30 countries in terms of per capita GDP. This would set an effective baseline at the bottom end. How low would the tax rate need to go to match the lowest number available? The lowest based on OECD data from 2005 is about 18% in S Korea. New Zealand is about 20% as well.

And the max could then be the maximum rate of industrialized countries. The number that I get from the OECD survey is 45% in Germany. Now I am not sure whether this is a net tax rate (pretty sure it is not, seems too high) or a marginal tax rate on the highest incomes (45% seems too low).

So a range between about 15% to 45% with the appropriate reasoning provided for Mins and Maxes seems to be the right answer in this case.</description>
		<content:encoded><![CDATA[<p>Great display of how putting a Min on the y-axis or setting a Max of 100% on the x-axis can give a misleading picture. It leads me to wonder what would have been right ways of showing this information. </p>
<p>Btw, I am not sure a line-graph does not produce the same misinterpretation. In several circles, line graphs, bar graphs and area plots are used interchangeably. People don&#8217;t necessarily pay attention to the fact that line graphs should be used mainly to depict time-series. </p>
<p>One possible Min could be the minimum tax rate in industrialized countries. It could be the min-rate in top 30 industrialized nations or the top 30 countries in terms of per capita GDP. This would set an effective baseline at the bottom end. How low would the tax rate need to go to match the lowest number available? The lowest based on OECD data from 2005 is about 18% in S Korea. New Zealand is about 20% as well.</p>
<p>And the max could then be the maximum rate of industrialized countries. The number that I get from the OECD survey is 45% in Germany. Now I am not sure whether this is a net tax rate (pretty sure it is not, seems too high) or a marginal tax rate on the highest incomes (45% seems too low).</p>
<p>So a range between about 15% to 45% with the appropriate reasoning provided for Mins and Maxes seems to be the right answer in this case.</p>
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		<title>By: Bob Gannon</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-16628</link>
		<dc:creator>Bob Gannon</dc:creator>
		<pubDate>Thu, 23 Jul 2009 19:03:50 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-16628</guid>
		<description>I think it would be more relevant to look at what percent of total federal tax revenues came from the top 1% of households and from each quintile.</description>
		<content:encoded><![CDATA[<p>I think it would be more relevant to look at what percent of total federal tax revenues came from the top 1% of households and from each quintile.</p>
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		<title>By: Andy Holaday</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-16586</link>
		<dc:creator>Andy Holaday</dc:creator>
		<pubDate>Thu, 23 Jul 2009 01:05:07 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-16586</guid>
		<description>My first impression was Jon&#039;s line chart tells the story most clearly. I immediately understood Clarke&#039;s &quot;area chart&quot; to be a line chart with shading fluff, but I had a harder time absorbing the interface between the light and the dark to gauge the measure of the trend. Possibly the slight change in the y-axis scale had something to do with my response. But, the y-axes in both of these charts span relevant values, which assuming the appropriate audience, should not be misinterpreted.

Kain&#039;s chart is clearly meant to deceive (glad he chimed in). Mike mentioned the problem with the distortion here as well. Any trend can be flat-lined by exaggerating the value axis beyond reasonable limits.</description>
		<content:encoded><![CDATA[<p>My first impression was Jon&#8217;s line chart tells the story most clearly. I immediately understood Clarke&#8217;s &#8220;area chart&#8221; to be a line chart with shading fluff, but I had a harder time absorbing the interface between the light and the dark to gauge the measure of the trend. Possibly the slight change in the y-axis scale had something to do with my response. But, the y-axes in both of these charts span relevant values, which assuming the appropriate audience, should not be misinterpreted.</p>
<p>Kain&#8217;s chart is clearly meant to deceive (glad he chimed in). Mike mentioned the problem with the distortion here as well. Any trend can be flat-lined by exaggerating the value axis beyond reasonable limits.</p>
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		<title>By: Jon Peltier</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-16574</link>
		<dc:creator>Jon Peltier</dc:creator>
		<pubDate>Wed, 22 Jul 2009 18:14:04 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-16574</guid>
		<description>I honestly had not considered this requirement of area charts myself, until Mr Joyner pointed it out. And I started to think, it doesn&#039;t matter. Then I realized that an &lt;em&gt;area&lt;/em&gt; chart uses area to help encode the data. So it&#039;s usually best to minimize opportunities to mislead your readers.

Unless that&#039;s your objective, of course.</description>
		<content:encoded><![CDATA[<p>I honestly had not considered this requirement of area charts myself, until Mr Joyner pointed it out. And I started to think, it doesn&#8217;t matter. Then I realized that an <em>area</em> chart uses area to help encode the data. So it&#8217;s usually best to minimize opportunities to mislead your readers.</p>
<p>Unless that&#8217;s your objective, of course.</p>
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		<title>By: Ducheznee</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-16573</link>
		<dc:creator>Ducheznee</dc:creator>
		<pubDate>Wed, 22 Jul 2009 17:27:40 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-16573</guid>
		<description>While I absolutely agree that column/bar charts must start from 0, I&#039;ve not considered the same argument for area charts (until you pointed it out here). Even at first glance I was not deceived by the Y-axis scale of Clarke&#039;s chart - that is one of the many chart elements I take note of immediately. But perhaps that simply indicates that some of your past lessons are finally sinking into my skull.</description>
		<content:encoded><![CDATA[<p>While I absolutely agree that column/bar charts must start from 0, I&#8217;ve not considered the same argument for area charts (until you pointed it out here). Even at first glance I was not deceived by the Y-axis scale of Clarke&#8217;s chart &#8211; that is one of the many chart elements I take note of immediately. But perhaps that simply indicates that some of your past lessons are finally sinking into my skull.</p>
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		<title>By: Jon Peltier</title>
		<link>http://peltiertech.com/WordPress/tax-the-rich-or-deceptive-axis-scales/comment-page-1/#comment-16569</link>
		<dc:creator>Jon Peltier</dc:creator>
		<pubDate>Wed, 22 Jul 2009 16:36:33 +0000</pubDate>
		<guid isPermaLink="false">http://peltiertech.com/WordPress/?p=2251#comment-16569</guid>
		<description>Gary -

You could use my routine to &lt;a href=&quot;http://peltiertech.com/WordPress/label-last-point-for-excel-2007/&quot; rel=&quot;nofollow&quot;&gt;Label Last Point for Excel 2007&lt;/a&gt;. Also, the way 2007 antialiases the magenta background makes it not completely disappear when it&#039;s assigned as a transparent color.</description>
		<content:encoded><![CDATA[<p>Gary -</p>
<p>You could use my routine to <a href="http://peltiertech.com/WordPress/label-last-point-for-excel-2007/" rel="nofollow">Label Last Point for Excel 2007</a>. Also, the way 2007 antialiases the magenta background makes it not completely disappear when it&#8217;s assigned as a transparent color.</p>
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