Donald Trump opened his 2016 presidential campaign with an epic rant against Mexican immigrants. “They are bringing drugs. They are bringing crime. They’re rapists,” said Trump, who added, “Some, I assume, are good people.” He went on to tell CNN that the threat lies not just with Mexican immigrants, but with immigrants in general. “You have people coming in, and I’m not just saying Mexicans, I’m talking about people that are from all over that are killers and rapists and they’re coming into this country,” Mr. Trump said.

Many observers have called these comments insensitive, discriminatory, and racist. Macy’s dropped the Trump line of clothing and Univision cancelled its broadcast of the Miss Universe pageant that he partly owns. Trump has doubled down on his remarks and claimed the mantle of a straight talker. Fellow presidential candidate Ted Cruz defended Mr. Trump because he “speaks the truth.” Rep. Steve King endorsed Trump’s comments and praised his “scrappiness.”

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America does indeed need leaders who are not afraid to tell the truth, especially when it comes to sensitive issues. But what are the facts about immigrants and crime?

Here is what you need to know: immigrants are less likely to commit crimes than people born in the United States. A 2013 Pew Research Center study found that across all people aged 12 to 24 (the teen and young adult years when almost all criminal activity first begins) immigrants were much less likely than the U.S.-born to have committed a crime in the last year.

Incarceration rates for young men tell the same story. The 2000 census shows that in all racial categories, immigrants are much less likely to be incarcerated than their U.S.-born counterparts. Men born in Mexico had an incarceration rate five times lower than the U.S.-born population as a whole.

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In California, home to the nation’s largest Mexican immigrant population (and the largest population of immigrants overall), a 2008 study by the Public Policy Institute of California found that the incarceration rate for immigrant adults was 297 per 100,000 in the population, compared to 813 per 100,000 among U.S.-born adults. Immigrants were less than half as likely to be incarcerated for drug crimes.

If immigrants were disproportionately likely to commit crimes, we would expect to see higher crime rates when and where immigrants arrive. Yet the opposite holds true. From 1994 to 2007, the number of immigrants per capita living in the United States rose from about 9 to 13 percent of the population. At the same time, FBI reports show that the rate of violent crime declined 34.2 percent. The property crime rate fell 26.4 percent.

Cities with large immigrant populations such as Chicago, Los Angeles, Miami, and New York also experienced declining crime rates during this period. The 2008 California study found that cities with relatively larger inflows of immigrants between 2000 and 2005 tended to see lower rates of violent crime. Contrary to the image of crime spilling across the border, FBI records show that rates of murder and other violent crimes are lower in U.S. cities within 100 miles of the border. The lowest murder rate of any U.S. city over 500,000 is El Paso, Texas.

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There is one prison system, of course, where immigrants are more likely to end up in custody than those born in the U.S. – it’s the federal prison system, where people who have broken immigration laws are housed. But even in this system, Trump’s statement prove false. Incarcerated immigrants are overwhelmingly held for low-level violations like entry and re-entry without inspection, not rapes and murders.

Why, then, is there the perception that more immigration causes more crime? At least part of the answer is that prominent conservative media personalities and politicians try to so hard to make a connection that isn’t there. A 2008 study found that of the discussions of illegal immigration on Lou Dobbs' television show the previous year, 52 percent mentioned crime, as did 45 percent of the discussion of illegal immigration on Bill O’Reilly’s show and 39 percent of Glenn Beck’s show.

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The American public deserves to hear straight talk about the issues that face the nation. But Mr. Trump is neither telling the truth nor simply being scrappy. He is appealing to the worst stereotypes of brown-skinned people who sell drugs to the children and rape the women. This isn’t straight talk, and it isn’t just insensitive. It’s false.