Misleading charts

It is well known that visual depictions of data can be misleading.

These deceptions are well known and much written about them.

This page looks at one such possible deception. Or is it?

Let us look at a headline from 2020-03-31 from the New York Times.

Opinion title: "Not winning this fight"
by David Leonhardt (Opinion Columnist)

Here is the introduction.

China and South Korea have flattened their curves. Italy, Spain, Germany and the Netherlands have begun to flatten their curves. The United States still has not.

Here is the chart, showing (absolute) data as reported from the U.S., Spain, Italy and China. Here is the Python code [#1]

import matplotlib.pyplot as plt
import rsPlot
domainList1 = [0, 4, 8, 12, 16]
rangeList1 = [
	[[0, 4, 18, 30, 42], "#990000", "China", 1439],
	[[0, 2, 5, 10, 27], "#009900", "Italy", 66],
	[[0, 2, 12, 52, 125], "#000099", "U.S.", 331],
	[[0, 2, 15, 25, 50], "#999900", "Spain", 47],
	]
# chart using original data
plot1 = rsPlot.plot("chart51-1",1,0,72,640,480)
print("Chart data: (original)")
for rangeList2,color1,country1,pop1 in rangeList1:
	s1 = str(rangeList2)
	print("")
	print("\t{0:s} : {1:s}".format(color1,s1))
	plt.plot(domainList1,rangeList2,color=color1,linewidth=4.0,label=country1)
plt.legend()
print("")
plot1.save()
# chart using adjusted data
plot1 = rsPlot.plot("chart51-1",1,0,72,640,480)
print("")
print("Chart data: (adjusted)")
for rangeList2,color1,country1,population1 in rangeList1:
	print("")
	rangeList3 = list(map(lambda x1: 1000.0*x1/population1,rangeList2))
	s1 = str(rangeList3)
	print("\t{0:s} : {1:s}".format(color1,s1))
	rangeList4 = list(map(lambda x1: float("{0:0.3f}".format(0).format(x1)),rangeList3))
	s1 = str(rangeList4)
	print("\t{0:s} : {1:s}".format(color1,s1))
	plt.plot(domainList1,rangeList3,color=color1,linewidth=4.0,label=country1)
plt.legend()
print("")
plot1.save()

Here is the output of the Python code.

(module rsPlot imported)
Chart data: (original)
	#990000 : [0, 4, 18, 30, 42]
	#009900 : [0, 2, 5, 10, 27]
	#000099 : [0, 2, 12, 52, 125]
	#999900 : [0, 2, 15, 25, 50]
	./chart51-1-01.png : 564 x 414 , 33,454 bytes
Chart data: (adjusted)
	#990000 : [0.0, 2.779708130646282, 12.50868658790827, 20.847810979847115, 29.186935371785964]
	#990000 : [0.0, 0.0, 0.0, 0.0, 0.0]
	#009900 : [0.0, 30.303030303030305, 75.75757575757575, 151.5151515151515, 409.09090909090907]
	#009900 : [0.0, 0.0, 0.0, 0.0, 0.0]
	#000099 : [0.0, 6.042296072507553, 36.25377643504532, 157.09969788519638, 377.64350453172204]
	#000099 : [0.0, 0.0, 0.0, 0.0, 0.0]
	#999900 : [0.0, 42.5531914893617, 319.1489361702128, 531.9148936170212, 1063.8297872340424]
	#999900 : [0.0, 0.0, 0.0, 0.0, 0.0]
	./chart51-1-02.png : 578 x 414 , 32,459 bytes

Note that when floating point divisions, the approximation leads to such printed numbers taking a lot of space. One can adjust this by displaying them rounded to a desired amount.

The original data uses an absolute scale.

The adjusted data uses a relative scale, as in per-capita, based on population.

Does it make a difference?

Looking at data in various ways to find patterns, etc., is often called exploratory data analysis.