When our brains don’t have a good intuition for reasoning with numbers, explicit probabilistic thinking can lead to improved decision-making.
“Mathematics has little surprises that are designed to test and push your mental limits The following 12 simple math problems prove outstandingly controversial among students of math, but are nonetheless facts.
“They’re paradoxes and idiosyncrasies of probability. And they’re guaranteed to start an argument or two. If you’re looking for a mathematical way to impress your friends and beguile your enemies, here’s a good place to start.”
This is an interesting case of how numbers get reported and what they mean. Often the numbers that get reported reflect a desire to grab people’s attentions or simply to tell the story the media outlet wants to tell. If you report 26% or 3% neither one is necessarily lying though the two numbers are referring to two different things. (Here is a link to an earlier post about how an Illinois tax increase was reported)
12% of respondents to a recent survey said they watched fewer NFL games and of those 26% said that the main reason was Colin Kaepernick’s protest during the national anthem. How should that get reported? And what impression gets left in people’s minds based on the wording?
Another way to think about it is this: 12% of the 26% who watched fewer games comes out to about 3% of the total number of people who watched football. Hmm. That leaves a very different impression than 26%.
Here is the original, misleading ESPN article whose headline has since changed I believe.
“National anthem protests were the top reason that NFL fans watched fewer games last season, according to a new survey released by J.D. Power.
“The pollster said it asked more than 9,200 people who attended either one football, basketball or hockey game whether they tuned into fewer games and why. Twenty-six percent of those who watched fewer games last season said that national anthem protests, some of which were led by Colin Kaepernick, were the reason.”
And here is a link to a Huffington Post article discussing the issue with how the numbers are reported:
“When they’re used well, graphs can help us intuitively grasp complex data. But as visual software has enabled more usage of graphs throughout all media, it has also made them easier to use in a careless or dishonest way — and as it turns out, there are plenty of ways graphs can mislead and outright manipulate. Lea Gaslowitz shares some things to look out for.”
“Carved into our past, woven into our present, numbers shape our perceptions of the world and of ourselves much more than we commonly think. Numbers and the Making of Us is a sweeping account of how numbers radically enhanced our species’ cognitive capabilities and sparked a revolution in human culture. Caleb Everett brings new insights in psychology, anthropology, primatology, linguistics, and other disciplines to bear in explaining the myriad human behaviors and modes of thought numbers have made possible, from enabling us to conceptualize time in new ways to facilitating the development of writing, agriculture, and other advances of civilization.
“Number concepts are a human invention―a tool, much like the wheel, developed and refined over millennia. Numbers allow us to grasp quantities precisely, but they are not innate. Recent research confirms that most specific quantities are not perceived in the absence of a number system. In fact, without the use of numbers, we cannot precisely grasp quantities greater than three; our minds can only estimate beyond this surprisingly minuscule limit.
“Everett examines the various types of numbers that have developed in different societies, showing how most number systems derived from anatomical factors such as the number of fingers on each hand. He details fascinating work with indigenous Amazonians who demonstrate that, unlike language, numbers are not a universal human endowment. Yet without numbers, the world as we know it would not exist.”