Why the numbers are not as objective as we think

Any dubious statement can be perceived as true if supported by statistics, tables, graphs and scientific terms. In order not to fall for such tricks, it is important to be able to recognize nonsense and generally understand what it is. A new book from the MIF publishing house "Complete nonsense!" will help with this. It was written by evolutionary biologist Professor Carl Bergstrom and assistant professor at the University of Washington School of Information, Jevin West. And Lifehacker publishes an excerpt from the fifth chapter.

Our world is literally digitized. Everything is calculated, measured, analyzed and evaluated. Internet companies track us online and use algorithms to predict what we will buy. Smartphones count our steps, measure the duration of calls, and track our movements throughout the day. Smart devices control how we use them and know more about our daily routine than we can imagine. Implanted medical devices feed a continuous stream of patient information and monitor for signs of danger in real time. During maintenance, our cars upload data about their performance and our driving style. The myriad of sensors and cameras installed in cities monitor everything from traffic flows to air quality, and are even capable of setting

personalities of passers-by.

Instead of gathering data about consumer behavior through costly surveys and surveys, companies let people come to them on their own and then record everything they do. Facebook* knows who we know. Google - what we want to find out. Uber - where we intend to go. Amazon - what we want to buy. Match - with whom we plan to create a family union. Tinder - from whom we are waiting for an invitation to communicate.

Data can help us understand the world in terms of objective facts, but data is nowhere near as objective as we think. An old joke comes to mind here. A mathematician, an engineer and an accountant get jobs. They are led into an office and given a math exam. The first task, for warming up: how much is two plus two? The mathematician rolls his eyes, writes "four" and moves on to the next tasks. The engineer thinks for a second, then writes "about four". The accountant looks around anxiously, then gets up from his chair, walks over to the person who testing, and in a hushed voice asks: “Before I write anything, tell me what you want get?"

Numbers are perfect for talking nonsense. They seem objective but can be easily manipulated to tell the right story.

Words are definitely produced by the human mind, but what about numbers? Numbers seem to be given to us by nature itself. We know that words are subjective. We know that they are used to twist and distort the truth. Words reflect intuition, feelings, passion. Numbers seem to exist separately from the person who talks about them.

People's faith in numbers is incredibly strong. Skeptics claim they "just want to see the data" or demand to be shown "baseline data" or insist that "the numbers should speak for themselves." We are convinced that “data never lie». But this view can be dangerous. Even if the values ​​or numbers are correct, they can still be used to fool the head […]. For numbers to be understandable, they must be in an appropriate context. They need to be demonstrated in such a way that an honest comparison is available to us.

Let's first think about where these numbers come from. Some of them we get directly, by precise counting or measurement. There are 50 states in the USA. There are 25 prime numbers less than 100. The Empire State Building has 102 floors. Baseball legend Tony Gwin hit 3,141 hits out of 9,288 at bat for a Major League batting average of .388. In principle, an accurate count should be fairly straight forward. There is a definite answer, and there is usually a certain calculation or measurement procedure that can be used to arrive at it. But this process is not always easy. It is quite possible to make mistakes in calculations, measurements, or in what exactly we consider. Take planets for example. solar system. From the time Neptune was discovered in 1846 until Pluto was discovered in 1930, we thought there were eight planets in the solar system. After the discovery of Pluto, we said that we have nine planets. Then, in 2006, the unfortunate "newcomer" was demoted to the status of a dwarf planet, and there were eight full-fledged planets orbiting the Sun again.

More often, however, accurate counts or exhaustive measurements are not possible.

We are not able to separately count each star in the observed Universeto arrive at the current trillion trillion approximation.

Similarly, we rely on rough estimates when looking at indicators such as the height of an adult in a particular country. Men from the Netherlands are considered the tallest in the world - an average of 183 centimeters. But in order to obtain these data, they did not measure all the inhabitants of the country and did not calculate the average of all the obtained values. Instead, the researchers used a random sample of local men, measured who fell into it, and extrapolated the findings to the entire population.

If one were to measure half a dozen men and calculate their average height, only by chance would the result be wrong. Suppose some of them were unusually tall. It's called sampling error. Fortunately, a large sample will usually even out the variances, so that such an error has minimal effect on the result.

Problems can also arise with the measurement procedure. Let's say the researchers asked participants to report their height, but men tend to inflate the numbers, with short men doing so more often than tall men.

Another source of error, the bias of the sample itself, is even more dangerous. Suppose you decide to determine the height of people, went to the local basketball court and began to measure the players. basketball playersis typically above average height, so your sample will not be representative of the general population and end up being too high. Most errors of this kind are not so obvious. […]

In these examples, we looked at groups of people over a range of values—for example, a range of heights—and then aggregated that information into a single number, called a summary statistic. For example, when describing a tall Dutchman, we are talking about average height.

Summary statistics can be a convenient way to summarize information, but if it's not correct, you can easily mislead your audience.

Politicians use this trick when they propose to introduce tax deduction, which will save hundreds of thousands of dollars for the richest 1% of citizens, but will in no way ease the tax burden of everyone else. They take the average tax deduction and claim that their tax plan will save families an average of $4,000 a year. Maybe so, but the average family—if we mean the one in the middle of the income distribution—will save nothing. Most of us will find it much more useful to know what the deduction for a family with a median income will be. In this case, the median is the “median” income between half of the families earning more than this value and half of the families earning less than this value. Thus, the median family will not receive any deduction at all, because it is only useful for the top 1% of the population with the highest incomes.

Sometimes we cannot directly measure the indicator that interests us. Carl recently came under the radar of the Highway Patrol on a straight and flat stretch of highway in the Utah desert, where for some inexplicable reason a speed limit of fifty miles per hour was set. He pulled over to the side of the road, glancing at the familiar flashes of red and blue lights in the rearview mirror. "Do you know how fast you were driving?" asked patrol. "I don't think so, officer," Carl replied. "Eighty-three miles an hour."

Eighty-three is a serious number, potentially threatening big trouble. But where did it come from? Some traffic cameras calculate your speed by measuring the distance you travel in a certain amount of time, but the state highways do it differently. The trooper was measuring something else—the Doppler shift in the radio waves emitted by his portable radar as they bounced off Carl's speeding car. The software embedded in the radar uses a mathematical model based on wave mechanics to calculate the speed of the vehicle using the measurements it receives. Since the patrolman does not directly measure speed Carla, the radar needs to be calibrated regularly. The standard way to get rid of a speeding ticket is to require the officer to show timely calibration records. True, Carl did not need it. He knew that he had exceeded the speed limit, and was glad that for his haste he got off with only a fine, albeit a large one.

Radars rely on very robust physical principles, but the models used to calculate other metrics can be more complex and involve more assumptions. The International Whaling Commission publishes data on the number of populations of some species of whales. When she reports that there are 2,300 blue whales in the waters of the Southern Hemisphere, she arrives at this number not because every one has been found and counted. animal. And they have not combed from and to some part of the ocean. Whales do not stand still, and most of the time they are not visible from the surface of the water. Therefore, scientists need indirect ways to determine the size of the population. For example, they count encounters with unique individuals that can be identified by markings on their caudal fins and tail. So their determination of whale numbers is as inaccurate as this technique is.

In calculations and facts that seem completely obvious, errors creep in for various reasons. You can get confused by the numbers. You can use too small a sample, which incorrectly reflects the characteristics of the entire group. The methods by which we derive numbers from other information may turn out to be incorrect. And finally, the numbers may simply be complete nonsense, invented from scratch in an attempt to give persuasiveness pathetic arguments. We must keep this in mind when we are being shown something by numbers. It is said that numbers never lie, but it should be remembered that they are often misleading.

"Complete nonsense!" talks about how misinformation spreads, why we believe in it and how to learn how to correctly assess causal relationships. This book proves that you don't have to be an expert in statistics to recognize fakes and changing concepts. Enough logic and critical thinking.

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