The How to Lie With Statistics Book Guide

This article is an excerpt from the Shortform book guide to "How to Lie With Statistics" by Darrell Huff. Shortform has the world's best summaries and analyses of books you should be reading.

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What can you learn from the How to Lie With Statistics book? What are the ten techniques that liars use to manipulate statistics? How can you assess if a statistic is reliable?

In his book How to Lie With Statistics, Darrell Huff explains how people (advertisers, companies, anyone with an agenda) can manipulate numbers to yield statistics that support their cause. Since these people aren’t actually lying, it isn’t considered illegal. Huff teaches you what to look out for and how to see through liars.

Continue on for more on How to Lie With Statistics.

How to Lie With Statistics

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 the How to Lie With Statistics book, 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.

Technique #1: Misleading With Bad Sampling

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.

Techniques #2-6: Fudging the Numbers (or the Point)

Technique #2: Citing Misleading “Averages”

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.

Technique #3: Giving Precise Figures to Appear More Reputable

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.)

Technique #4: Using Percentages to Hide Numbers and Calculations

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 weren’t directly comparable.

3. Adding up percentages. Percentages aren’t numbers—you can’t meaningfully add or subtract them.

For example, imagine you buy 20 vegetables at the grocery store and all of them cost you 5% more than they did last year. If you add together all of those 5% increases, you get a 100% increase (20*5%=100%). This could be reported as “the cost of living has gone up by 100%.” But in reality, it hasn’t—it’s gone up by 5%, and all products were affected.

4. Giving percentage points instead of percentages to confuse people. Percentage points are the difference between two percentages. For instance, the difference between 5% and 7% is two percentage points. If a liar doesn’t want to report how much money her company made, and her return on investment was 3% last year and 6% this year, she might say “return on investment rose three percentage points.” A three-point increase sounds much smaller than a doubling, even though they mean the same thing in this case.

Technique #5: Omitting Statistical Qualifiers

The last way to fudge numbers is to leave out information that puts caveats on their accuracy or further explains them. There are four types of information liars often neglect to include with their figures:

1. Probable error. Probable error is a measure of how reliable a figure is, expressed as a range that the true result will fall between. (It’s impossible to find the single number that represents the true result because measuring systems aren’t perfectly accurate.) Therefore, if you’re presented with a single figure, and aren’t given any indication of how accurate it is, it may not be accurate at all.

For example, if an IQ test has a probable error of 3 and you score 98, this means that your IQ is somewhere between 95-101 (98-3=95, and 98+3=101). The real number is equally likely to be any number in that range. So, simply telling someone that your IQ is 98 isn’t accurate.

2. Degree of significance. The degree of significance is a measure of how likely it is that results are due to chance. In most cases, for a figure to be statistically significant, the degree needs to be no more than 5%—this means that 95 out of 100 times, the results are real and not attributable to chance. If the degree isn’t given, it may be higher than 5%, which means the results could be due more to chance than anything else.

3. What the comparison is to. Some stats promise to “triple” the effectiveness of a product, or offer “25% more,” but don’t say what they’re compared against. A granola bar that contains 25% more protein than a competitor’s, versus a bar that contains 25% more protein than a rock, are two entirely different things.

The How to Lie With Statistics Book Guide