# Wrong Number: How to tell fact from fiction in a world full of bogus data

Here’s a pop quiz: Which of these public statements contained incorrect or misleading numbers?

• “Add that to Marco’s plan for a trillion dollars in new military spending, and you get something to me that sounds not very conservative.” ― U.S. Sen. Rand Paul, speaking about Sen. Marco Rubio during a 2015 Republican Presidential Debate.
• “Just last year we gave the military a \$700 billion budget increase, which they didn’t even ask for.” ― U.S. Rep. Alexandria Ocasio-Cortez, then a House candidate, in July 2018 on The Daily Show with Trevor Noah.
• “They said, ‘You know we could make it smaller. ‘We could make it 3 percent, we could make it 2 percent, we could make it 4 percent.’ I said, ‘No, make it 10 percent, make it more than 10 percent.‘ ”  ―  President Donald Trump on military pay increases during a December 2018 visit to Iraq.

The answer is … every one of those statements was incorrect or misleading.

On this episode of Numbers Geek, we’ll talk with someone who specializes in recognizing “bogus and misleading” numbers in media coverage and public statements: Brian Kernighan, a Princeton University computer science professor and the author of a new book, “Millions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers.”

The book arose from a class that he teaches at Princeton about computing and communications for non-technical students. He uses the mistakes as real-world examples to help the students learn to detect errors.

Among the techniques Kernighan suggests:

• Ask yourself what the implications of a particular number would be, if accurate. Kernighan cites the example of a news article suggesting energy savings of \$88 per day if people turned off their computer monitors every night. In reality, that was the savings per year. Few people could afford to run a computer if that number was true.
• Break a number down to one person’s share of the number, and ask if the number makes sense on that scale. For example, a useful number to know for context is 325 million, the approximate population of the United States. An effective technique is to divide numbers by 325 million (or even 300 million to get in the ballpark) and asking if the result per person is reasonable
• Consider numbers as a percentage of larger known numbers. For example, it’s often useful to look at numbers as a percentage of total state, local and government spending of about \$5.7 trillion.

That last technique helps us fact-check the statements above about U.S. military spending and pay.

National defense spending in 2017 totaled \$728.9 billion, a decrease from \$916.6 billion in 2010 (adjusted to 2016 dollars for comparison) These numbers ebb and flow with U.S. military engagement in overseas conflicts. Defense spending is about 13 percent of total federal, state and local government spending.

• In the case of Ocasio-Cortez’s statement, she mistakenly referred to the total size of the military budget rather than the budget increase. To her credit, her campaign acknowledged afterward that she misspoke, although the Daily Show video of the misstatement remains uncorrected.
• What about Rand Paul’s statement that Marco Rubio wanted to increase military spending by a trillion dollars? That seems out of proportion given that the entire budget is \$717 billion under the plan approved by Congress. It turned out that Paul was referring to Rubio’s planned increase over 10 years, which Paul didn’t say.
• Trump’s statement on military pay was incorrect. The pay raise authorized in the 2019 budget was 2.6 percent. Total military compensation per active duty servicemember has grown from \$59,000 in 1980 to \$113,000 in 2016, after adjusting for inflation. This number includes salary and all benefits. Compensation of personnel represents 33 percent of military spending.

Listen to the full episode above, and for a deep dive on U.S. military spending, see USAFacts.org and pages 35-38 of the 2018 USA Facts annual report.