Leaf Van Boven is professor of psychology at the University of Colorado, Boulder. Paul Slovic is president of Decision Research and professor of psychology at the University of Oregon.

On January 16, President Donald Trump tweeted a summary of a government report showing that “nearly 3 in 4 individuals convicted of terrorism-related charges are foreign born.” The report, issued by the departments of Justice and Homeland Security, noted that from September 11, 2001, to December 31, 2016, of the 549 people convicted of international terrorism-related charges in U.S. federal courts, 402 were foreign born.

The White House fact sheet accompanying the report concluded: “TIME TO END CHAIN MIGRATION AND THE VISA LOTTERY: This report shows, once again, that our current immigration system jeopardizes our national security.” Attorney General Jeff Sessions struck a similar chord, declaring that “our immigration system has undermined our national security and public safety,” and that “we currently have terrorism-related investigations against thousands of people in the United States, including hundreds of people who came here as refugees.”


Yet using the “nearly 3 in 4” statistic to imply that the U.S. immigration system increases terrorist threats is a deeply misleading tactic. It exploits a psychological challenge that most of us face in reasoning about risk—with potentially disastrous consequences, especially as immigration policies are being debated and lives hang in the balance.

Criticism of the report so far has focused on the specific numbers cited. For example, the report does not include domestic terrorists, who are less likely to be foreign born. The report also concerns terrorism-related convictions—activities such as perjury and petty theft that are often tenuously connected to terrorist attacks themselves. Plus, the report includes foreign-born individuals extradited from other countries for prosecution in the United States. All of which suggests the “nearly 3 in 4” statistic is inflated.

But there is a more fundamental problem with thinking about terrorist risks in this way. The 75 percent statistic ignores the rarity of terrorist-related activities despite the very large number of foreign-born individuals in the United States. Treating 75 percent as a meaningful measure of risk is deceitful—it’s lying with statistics.

To see why, consider a less politically charged domain. Of the approximately 450 NBA players, about 330 are African-American—a fraction close to 3 in 4. But among more than 20 million African-American men in the United States, a vanishingly small portion play in the NBA—less than 0.01 percent. In other words, we can be about 75 percent confident that a man is African-American if we know he is an NBA player. But if we know only that a man is African-American, we can be even more confident that he is not an NBA player.

Similarly, we can be confident that an individual convicted of terrorism-related charges in a U.S. federal court is foreign born (a probability of about 75 percent). But if an individual is foreign born, the likelihood that the person has engaged in terrorism-related activities is nearly zero. There are approximately 41 million foreign-born people living in the United States; 402 out of 41 million is a minuscule proportion—less than 0.001 percent.

Even though the numbers are vastly different, people often treat these two types of statements about probability as though they are equally valid. Psychologists call this an inverse fallacy. It arises from natural human tendencies in responding to risk.

One issue is that inverted probability statements sound the same. The “likelihood of a terrorist being an immigrant” uses almost the same words as the “likelihood of an immigrant being a terrorist.” Without carefully reflecting on the validity of such claims, people might not appreciate the difference between phonetically similar phrases.

The inverse fallacy may be especially pronounced in the context of terrorism. People perceive risk based largely on emotion, and terrorism is unquestionably frightening. Alarmingly high numbers like 75 percent jibe with people’s fear of terrorists, many of whom are foreign born. The dread of terrorism is discordant with the minuscule proportion of foreign-born individuals who are terrorists.

These feelings of dread are stoked by politicians’ extensive use of anecdotal evidence. The White House report includes eight “illustrative examples” of individuals who were among the 402 convicted of terrorist-related activities. Descriptions of individual cases are more emotionally evocative than descriptions of statistics, and this affects how individuals are treated: People are more inclined to punish identified perpetrators than statistical perpetrators, just as they are more inclined to help identified victims than statistical ones.

The persuasiveness of misused inverted probabilities presents a puzzle. We suspect nearly everyone can appreciate that the fraction of African-American men who play in the NBA is nearly zero—and that the fraction of foreign-born individuals in the United States who are terrorists is nearly zero. So why don’t people correct these misconceptions? One reason is that people are loath to scrutinize statements that confirm what they already believe. People are particularly receptive to believe statements from trusted sources (the departments of Justice and Homeland Security, if not the president). If people already believe that immigrants pose a threat, they are unlikely to probe whether the White House is phrasing its statistics appropriately.

Confusing the inverse probabilities of terrorist acts and foreign-born individuals is not merely an academic issue. Proponents of restrictive immigration polices continue to use fear-based, inverse fallacy tactics. During the recent government shutdown, Trump released an ad promising to “fix our border and keep our families safe,” adding, “Democrats who stand in our way will be complicit in every murder committed by illegal immigrants.”

Citing that “3 in 4” terrorists are foreign born implies, erroneously, that excluding the foreign born would substantially reduce a large threat to this country. But at what cost? How many of the 41 million lives of immigrants and refugees should be ruined to further reduce an already minuscule threat? Let’s not use statistical lies to destroy lives.