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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How do liars manipulate statistics to make them more favorable? How can hard numbers possibly be skewed?
Manipulating statistics isn’t as difficult as one may think. Although statistics are hard numbers and lying about them isn’t legal, that doesn’t mean they can’t be skewed or framed in a way to make the presenter look better.
Keep reading for the top eight ways that statistics are manipulated.
How Liars Manipulate 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. Manipulating statistics seems impossible, right? Wrong.
Statistics aren’t as objective as they seem. 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.
Here are the top eight techniques that anybody with an agenda can use to manipulate statistics in their favor:
Technique #1: Citing Misleading “Averages”
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.
This is a useful average for liars to use because it allows them to:
- Make the number look bigger and better. 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 will make the mean look higher than any of the other averages.
- Hide inequality. If 90 employees at a company are paid $20,000 a year and the boss is paid $200,000, the mean is ((90*20,000)+(1*200,000))/91=21,978. The mean doesn’t show that one person is paid a lot more than everyone else.
In turn, hiding that they’re using the mean, by simply using the more general “average” to describe the figure, benefits liars by obscuring the fact that they’re using such an unreliable calculation.
Technique #2: Giving Precise Figures to Appear More Reputable
Another number-fudging technique is to include a decimal to make a figure look more precise and therefore reputable. (For example, reading that most people sleep 7.84 hours a night sounds a lot more impressive than “about eight hours.”)
Liars can get decimals by doing calculations (for example, calculating the mean) on inexact figures that weren’t measured to the decimal point.
Technique #3: 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.
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.
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.
Liars can also combine percentages and averages while manipulating bases to mask the real data even more. For example, if milk has gone down from $2 a pint to $1, but bread has gone up from $1 to $2, liars can massage percentage math and choose different bases to prove the cost of living has gone up or down, depending on their agenda. To show costs went up, they can decide that last year’s prices were the base (100%). Milk’s price has halved (50%) and bread’s price has doubled (200%). The average of 50% and 200% is 125%, so prices have increased by 25% since last year.
To show costs went down, they can decide that this year is the base year (100%). With this base, milk used to cost 200% more and bread cost 50% less—you get the same average of 125%, but since the base is different, it shows a decrease of 25% since last year.
3. Adding up percentages. Percentages aren’t numbers—you can’t meaningfully add or subtract them.
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 #4: Using the Most Favorable Form
The fourth technique is to report numbers in whatever form most exaggerates or minimizes them; whichever will further a liar’s agenda. For example, return on sales, return on investment, and increase or decrease in profits are all ways of reporting how much money a company made. Most people won’t realize that each type of measure tells only part of the story. For example, if you buy a stock every morning for $99 and sell it in the afternoon for $100, you’re making only 1% on total sales, which doesn’t sound like a great return. However, over 30 days, you’re making 30% on total money invested—a much better-sounding prospect.
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:
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- The 10 ways you might end up fooled by statistics
- How to differentiate between legitimate and lying statistics
- Why you can't even trust a graph
