DaveWentzel.com All Things Data
How To Deceive With Charts and Graphs - Part 2
Submitted by Dave Wentzel on Wed, 2010-11-24 10:19
In Part 1 I covered using statistics inappropriately for qualitative analysis.
Take a look at the following graphic from a typical "Stocks in the News" section of The Wall Street Journal.
Take Exxon Mobil specifically. It's at $91 and the movement is about 1% over the sample period. Yet the graph's min and max is $50 and $125. Given the data plots for Sept to Dec the range never fluctuates out of the $75-$100 band. Should we infer that further in the past the range was wider? We don't know. A better graph would have a range of $75-$100 so the reader could more closely see any potential trend or volatility, at least in the short-term. Yet these WSJ charts are still presented this way...to this day.
You can take this too far though. Suppose you were the author of the accompanying article about ExxonMobil and you owned a ton of shares. You want your shares to rocket higher from readers getting excited from the graph. How do you do that? Take the Y axis and shrink the band further to a range of $85-$95 and then shrunk the X axis to just Nov-Dec. That would really look like a rocket stock!!!
Here is an example using a LoadRunner graph.
Here we have a dual scale graph. The scale on the right lists the number of vusers for the given test. It is the green line that is almost off the top of the graph. That's generally not good scale...leave a little white space on the top and bottom of your scale. To make matters worse the left scale quantifies the resource usages shown by all of the other lines plotted on the graph...and they are cramped into the bottom 2/7's of the graph (no value rises above 2) making this even more unreadable.
Y Axis Manipulation
I'm sure you've seen graphs where the Y axis does not start at 0...but has a "break mark" on the axis to indicate the fact. For instance, a DJIA chart of the past 10 years might show a range of 5000-15000 yet the Y axis will start at 5000. The "break mark" will indicate to the observer that the graph is not to scale. This is the correct way to display this type of graph.
In other cases, such as magazines that may want to show trends in the Dow, will not show the break mark and will just start at 0. This means the bulk of the graph is meaningless since the Dow's movement occurred in the narrow band of 5000-15000...the first 5000 are meaningless.
However, sometimes the break mark is not included purposefully to deceive. Consider this gold graph.
A cursory look may lead you to believe that South Africa's percentage share of world gold production has increased up to 1983. But you'd be wrong. Why? First, note the Y axis starts at 10, not 0, and the graph has no break mark. On a percentage basis, South Africa's production hasn't really changed. In 1950 South Africa produced about 13 million out of 28 million ounces (46%) and in 1980 they produced about 20 million ounces out of 45 million, for about 44% of world production. The chart sure doesn't tell me that!!! On a percentage basis this chart is telling that the communists (centrally planned economies) are producing a greater percentage of total ounces. This is a poor graph to tell us that though.
Charts Without Any Scale
Take the following chart:
This is the famous "Laffer curve" which is used as the basis of Reagonomics. Do a google search if you want to read more. Whether or not you agree with supply-side economics, the chart has some major flaws which are what I want to focus on.
A quick background. The thought is that there is a magical tax rate where a government can collect the maximum amount of revenue. If the rate is too high there is a disincentive to work, hence tax revenues drop off. If the rate is too low, some people work as much as possible, but mostly the government is not collecting as much as it could.
What's the problem with the chart? Well, what is that maximum tax rate? No one knows. The chart is good to discuss theoreticals, but doesn't help us pragmatically. If you want to show theory then a chart without numbers is OK, and that's really the only time it is acceptable.
I can't help but give you my thoughts here. First of all, supply siders will state that lower taxes will always generate more tax revenues, hence we should lower the tax rates. As you can see with the Laffer Curve, this really is NOT the case, unless you believe people work harder when rates are lower, hence adding to the revenue pool. I don't believe this. Supply-side economics is just another tax hike meant to fool you. A tax is a tax and Reagan never did lower spending...he actually increased it, causing huge deficits. Just my opinion but the best policy matches closer to the Austrians (www.mises.org).