The way we evaluate ideas and approach problems is greatly influenced by how they are presented to us. Even slight changes in the wording or focus of a statement or question can significantly impact our responses. An excellent example of this phenomenon is evident in how we assess risk. While you might expect that once we can determine the probability of a risk, everyone would respond the same way, this is not the case. Even when probabilities are precisely calculated, altering how the information is framed can lead to different responses.

For instance, people are more likely to perceive a rare event as likely to occur if it is expressed in terms of relative frequency rather than as a statistical probability. In the Mr. Jones experiment, two groups of psychiatric professionals were asked about the safety of discharging Mr. Jones from a psychiatric hospital. The first group was informed that patients like Mr. Jones had a “10 percent probability of committing an act of violence,” and the second group was told that “of every 100 patients similar to Mr. Jones, 10 are estimated to commit an act of violence.” Surprisingly, almost twice as many respondents in the second group opposed his discharge.

Another cognitive bias that diverts our attention from statistically relevant information is known as Denominator Neglect. This occurs when we overlook plain statistics in favor of vivid mental images that influence our decisions. Consider these two statements: “This drug protects children from disease X but has a 0.001 percent chance of permanent disfigurement” versus “One out of 100,000 children who take this drug will be permanently disfigured.” Despite both statements having equal mathematical weight, the latter conjures a mental image of a disfigured child and has a more profound impact, making us less likely to administer the drug.