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How to Lie With Statistics by Darrell Huff.

Read Full SummaryHow to Lie With Statistics by Darrell Huff.

**When searching for the truth, statistics are appealing—they seem like hard, believable numbers**, and they’re necessary for expressing certain information, such as census data.

However, **statistics aren’t as objective as they seem.** In *How to Lie With Statistics*, author Darrell Huff explains how people who want to conceal the truth manipulate numbers to come up with statistics that support their positions. These people—advertisers, companies, anyone with an agenda—often don’t even have to actually *lie*. Statistics is a flexible enough field that would-be liars can make their case with implications, omissions, and distraction, rather than outright falsehoods.

**Not all bad statistics are manipulations or lies, of course.** Some are produced by incompetent statisticians; others are accidentally misreported by media who don’t understand the field. However, because most mistakes are usually in favor of whoever’s citing the statistic, it’s fair to assume that a lot of bad statistics are created on purpose.

In this summary, you’ll learn the techniques shady characters use to lie (or imply) with statistics. You’ll also get a five-step questionnaire for evaluating the legitimacy of statistics you come across.

To get their numbers, honest statisticians count a sample of whatever they’re studying instead of the whole (counting the whole would be too expensive and impractical) and take steps to make sure the sample’s make-up accurately represents the whole. They do this by making sure the sample is large (this reduces the effects of chance, which only has a negligible impact on large samples) and random (every entity in the group must have an equal chance of being part of the sample).

On the other hand, **liars purposely take samples that don’t accurately represent the whole to engineer the results that they want. Or, they take small samples so that chance gives them the results they want.**

- For example, if a liar wants to say that her toothpaste reduces cavities, she might ask 12 people with healthy teeth (as opposed to a group of people with a variety of dental health levels) to start using it. If this group of 12 doesn’t show any reduction in cavities, she can try the same experiment with another group of 12. Since the only possible outcomes of using toothpaste are getting more cavities, fewer cavities, or the same number of cavities, eventually the 12-person sample will by chance all (or mostly) hit on a reduction in cavities. This is much less likely to happen in a sample of, say, 120 people.

Liars often use **the word “average” without specifying what kind of average a figure represents. **For instance, they may use it to refer to mean—the number that’s the result of adding up all the sample’s numbers and then dividing by the number of samples.

- (Shortform example: To get the mean income of five people, you’d add up all their incomes and divide by five: 30,000+30,000+50,000+60,000+70,000=48,000.)

Giving the mean is advantageous for liars because it hides large inequalities.

- (Shortform example: If 90 employees at a company are paid $20,000 a year and the boss is paid $200,000, the mean pay is ((90
*20,000)+(1*200,000))/91=21,978. The mean hides that one person is paid a lot more than everyone else.)

In turn, *hiding* that they’re using the mean, by simply using the word “average” to describe the figure, benefits liars by obscuring the fact that they’re using such an unreliable calculation.

Another number-fudging technique is to **include a decimal in a statistic to make a figure look more precise and therefore reputable.** Liars can engineer decimals by doing calculations (for example, calculating the mean) on inexact figures** **that weren't measured to the decimal point.

- (Shortform example: If you ask 100 people how much they spent on groceries in the last month, they probably won’t remember exactly. Even if they give you round, approximate numbers, if you calculate the mean, you’ll likely end up with a decimal. For instance, (20+30+60)/3=36.66666... This number is meaninglessly more precise than the measures you started with, but it looks good.)

Like decimals, giving percentages instead of raw figures can make numbers look more precise and reputable than they really are. (Shortform example: If two out of three people prefer a certain cleaning product, this can be expressed as 33.333…%. The decimal adds precision and implies reputability.)

Here are some additional ways liars manipulate percentages and their associated terms for their gain:

**1. Hiding raw numbers and small sample sizes.** Percentages don’t give any indication of the absolute value of raw figures, so liars can use them to mask unfavorable numbers or suspiciously small sample sizes.

- (Shortform example: If a stock was worth $1 yesterday and $2 today, that’s a 100% increase, which looks impressive. However, the actual difference is only $1, which looks unimpressive.)

**2. Using different bases.** Because percentages don’t give any indication of the raw figures (bases) used to calculate them, liars can compare percentages calculated off different bases to distort their results.

- For example,
*The New York Times*once reported that after taking a 20% cut last year, union workers got a 5% raise the next year, which gave them back*one-fourth of their cut wage*. This claim of it being one-fourth of their cut wage refers to 5% being one-fourth of 20%. However, the workers didn’t actually get 5% of their*original*wage back, they got a 5% increase on their*new, lower*wage, which is a smaller number. The 20% cut and the 5% increase were calculated off different bases, so...

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Here's a preview of the rest of Shortform's How to Lie With Statistics summary:

**When searching for the truth, statistics are appealing—they seem like hard, believable numbers**, and they’re necessary for expressing certain information, such as census data. Many people take statistics at face value because they suspend their common sense when presented with numbers, panic at the thought of complicated calculations, or feel math can’t lie.

However, **statistics aren’t as objective as they seem.** In *How to Lie With Statistics*, author Darrell Huff explains how people who want to conceal the truth manipulate numbers to come up with statistics that support their positions. These people—advertisers, companies, anyone with an agenda—often don’t even have to actually *lie*. Statistics is a flexible enough field that would-be liars can make their case with implications, omissions, and distraction, rather than outright falsehoods.

**Not all bad statistics are manipulations or lies, of course.** Some are produced by incompetent statisticians; others are accidentally misreported by media who don’t understand the field. However, because **most mistakes are usually in favor of whoever’s citing the statistic, it’s fair to assume that a lot of bad statistics are...

In the last chapter, you learned how people manipulate samples to get favorable stats. Now, you’ll learn how liars pull or imply favorable numbers from existing data, without even having to change anything about the sample.

There are five techniques for fudging numbers:

The first technique is **using the word “average” without specifying what kind of average a figure represents. **Each kind is calculated differently and gives different information (and a different impression) about the data:

**Average Type #1: Mean. **This number is the result of adding up all the sample’s numbers and then dividing by the number of samples.

- (Shortform example: To get the mean income of five people, you’d add up all their incomes and divide by five: ($30,000+$50,000+$70,000+$70,000+$70,000)/5=$58,000)

This is a useful average for liars to use because it allows them to:

**Make the number look bigger and better.**(Shortform example: If a university wants to attract students, the larger the average income of its graduates, the more attractive it looks to prospective students. Even if there are just a few high salaries, the math...

This is the best summary ofHow to Win Friends and Influence PeopleI've ever read. I learned all the main points in just 20 minutes.

There are five techniques liars use to fudge the numbers.

Imagine you read that the average income of an Ivy League graduate is $70,562. What lying techniques were possibly used in generating this stat? How do you know?

In the previous chapter, you learned how liars massage math to make their results look more favorable. If liars can’t find a calculation that gives them figures they like, another technique they use is to focus on *other* figures that *do* seem to support what they have to say.

There are two techniques liars use to do this:

If liars can’t prove something, sometimes, **they’ll prove something else that sounds like it's the same as what they were trying to prove. **

- For example, if a cold medicine company can’t prove that their drug cures colds, but they can prove that it kills germs in a lab, they might advertise that their medicine “kills 15,000 germs.” Killing germs
*isn’t*the same as curing colds (colds probably aren’t even caused by germs), but they’re close enough that people might think the medicine actually works.

Note that **in some cases, the semi-related figure can actually give a more accurate picture of the situation than the direct figure.**

- For example, the number of deaths a disease has caused is often a better indication of its incidence than the number of cases of it, because the record-keeping...

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In the previous two chapters, you learned seven techniques liars use to present numbers in the most favorable light. Now, we’ll look at another way they misleadingly report numbers—in images.

Here are some ways that liars lie in graphics. They:

**1. Truncate the graphs.** To make changes look larger than they are, liars remove the empty space on a graph so that the part the data occupies is the only part shown. This will make the slope of a line look steeper, or the difference between bars look greater.

- For example, from this graph, it’s clear that profit is steadily growing:

On this truncated graph, however, it appears that profit is *rapidly *growing, because the empty space is gone:

**2. Add more divisions to the y-axis. **Like truncation, this will visibly amplify the differences between measures.

- For example, from this graph, it’s obvious that there’s little difference in profit from year-to-year: ...

There are many techniques liars use to make graphs misleading.

Which of the liars’ techniques do you spot in the line graph below?

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In the previous three chapters, you learned some of the strategies liars use to mislead people with statistics. Now, you’ll learn about a five-question checklist you can go through every time you encounter a statistic to assess its legitimacy. The goal is to find balance—**you don’t want to swallow statistics without thinking about them** (it’s often worse to know something wrong than to be ignorant), **but you also don’t want to be so suspicious that you ignore all statistics and miss out on important information.**

Here are the evaluation questions:

The first thing to do **when confronted with a statistic is to figure out where it’s coming from.** The source may not be obvious, because liars often borrow the numbers of reputable organizations, such as universities or labs, but come to their own conclusions. Then, they try to make it look like *their *conclusion is the reputable organization's conclusion. Always be suspicious of the phrase “the survey/study shows”; *who says *that the survey or study shows this?

- For example, in an article about how women who attend college have a higher likelihood of becoming old...

There are five questions to ask when you encounter a statistic to assess its legitimacy.

Consider this statistic published by a company selling blue wallpaper: “According to a survey of parents conducted by our company, an average of 97.68% of infants cry when in a room with green-colored wallpaper. Therefore, most infants hate living in homes with green wallpaper.” What is the original source of this stat? How might this affect its reliability?

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