2.6: Misleading Graphs
- Page ID
- 105818
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Next, we are going to discuss visual summaries that do not serve the purpose of telling the story but rather confuse or mislead.
Case 1.
Look at the massive decrease in unemployment from September of one year to March of the following year!
The unemployment decrease looks significant on the histogram only due to most of the histogram missing due to the cutoff on the vertical axis.
If you look at the whole picture the decrease from 5.4% to 5.0% does not seem that impressive!
Case 2.
Look at the huge difference between the effects of OxyContin and Placebo!
As in previous case, the difference between the effects looks significant on the histogram only due to most of the histogram missing due to the cutoff on the vertical axis.
And as in the previous case, if you look at the whole picture the decrease from 5.4% to 5.0% doesn't seem that impressive!
Case 3.
Look at the massive increase in home prices from 1998 and 1999!
Hopefully, nobody is fooled by this image and the narrative. If you look at the numbers only - the increase from $80000 to $82000 does not seem that impressive!
Case 4.
Please do not think that this can only happen in a textbook. This is an example of a newspaper with a misleading graph! Can you tell which graph is a misleading one?
Case 5.
Of course, this can also be found on the web. Here is another example of a misleading graph!
Case 6.
You can find many such examples in major news networks or at least one network – coincidentally all the examples here are from FOX NEWS.
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Case 7.
Look at the proportion of smoking adults decreasing from 1970 to 2013!
While the proportion of smoking adults decrease by a factor of 2, the problem with this visual demonstration is that when the dimensions are increased/decreased by a factor of 2 the area is increased/decreased by a factor of 4, so in this case, it appears that the proportion decreased by a factor of 4.
Case 8.
Look at how much more the basketball is more expensive to attend in comparison to the other sports!
While the average ticket prices for basketball event is the highest at $38 in comparison to $17 for the other sports, the images of a puck, a baseball, and a basketball put the focus on the area rather than the height which is rather distracting than revealing.
Case 9.
What a great 3D pie chart! But …
Which of the two categories - local passenger transport or food - appears bigger? Food? Wrong, they are both 12%! With the recent advancements in technology, it is very easy to produce a 3d image with a press of a button, however rarely the use of such graphs is justified. So be aware!
Case 10.
Another example of a great 3D summary! But …
Which of the two categories - 1 or 4 - appears taller? 4? Wrong, they are both 0.5!
Case 11.
Wow, look at this chart! The economy is clearly doomed!
Oh, never mind, this is the heat map of a microwave after using it for 1 minute! The problem here is that no axes are labeled, and it is hard to guess what the chart represents! Please, never hesitate to question the labels and the units!
Case 12.
Sometimes the visual summary misrepresents the data by mistake as in the next case:
Do you think the majority of voters think that Scotland should be independent? Wrong! The other majority thinks otherwise!
Case 13.
However, sometimes the visual summary misrepresents the data with an ill purpose as in the next case:
How do you think the number of murders committed using firearms changed after Florida enacted its “stand your Ground” law? It appears that the number went down however look at the flipped vertical axis!!!