(MONEY Magazine) – When college students were asked which was riskier, a kind of cancer that kills 1,286 out of 10,000 people it strikes or one that kills 12.86% of them, the students rated the first kind about 20% more dangerous. A knock on college kids? Not really. Our perceptions are so dominated by our emotions that a small change in the way a risk is presented to us can have a big impact on how scary it seems.

"Equivalent ways of describing something should lead to equivalent judgments and decisions," says University of Oregon psychologist Paul Slovic, an authority on how we assess risk. "But it's not true. People's judgments about risk are very movable and subjective."

When researchers told psychiatrists that "20 out of every 100 patients similar to Mr. Jones are estimated to commit an act of violence" within six months of being released from a mental hospital, only 59% said they would release him. But when told that "patients similar to Mr. Jones are estimated to have a 20% chance of committing an act of violence," 79% said they'd release him. What's going on? Vivid imagery lights up our emotions, shoving analysis aside. As Slovic puts it, "If you tell someone that something will happen to one out of 10 people, they think, 'Well, who's the one?'"

You may act differently if your financial adviser tells you that you have an 80% chance of hitting your retirement goals than you will if he tells you that one out of five people in your situation ends up eating cat food. Either way, he's given you the same number.

Emotional responses to data also trip us up when we try to assess benefits, studies show. Workers are happier getting a 7% raise when inflation is at 5% than they are receiving a 5% raise when inflation is running at 3%. Shoppers think they're getting a better deal at a two-for-one sale than at a 50%-off sale. And investors get giddy over stock splits even though the value of their holdings doesn't change. Here's how you can stop playing number tricks on yourself in your own investing.

» Look at lots of data. When you shop for a stock or mutual fund, don't rely on "average return" or get sucked in by a big cumulative number like a return of 2,900% over 10 years. That would be the return on Dell's stock, which is down 15% during the past five years.

» Get a second opinion. It's hard to get impressive-sounding numbers out of your head. Ask someone you respect to look at the data too before you decide to buy.

» Sleep on it. Your short-term moods can wreak havoc on your judgment of long-term risks. So wait a day before a final decision.