The Impact Number Formats Have on Judgment and Decision Making

Frequencies Versus Percentages

In another study, researchers asked experienced forensic psychologists and psychiatrists to determine the likelihood that a mental patient would commit an act of violence within six months after being discharged from the hospital. [4] They split the respondents into two groups and

• gave one group data in the form of relative frequencies—for example, telling them that 20 out of every 100 mental patients typically commit a violent act after their release from a hospital
• gave the other group data in the form of statistics—for example, that there is a 20% chance that mental patients will commit a violent act after their release.

Which group do you think considered mental patients more dangerous? It turned out that 41% refused to discharge a patient when given the data as a frequency, while 21% refused to discharge a patient when given the data as a probability. Why do you think there was a difference?

Researchers concluded that when people thought about the scenario in terms of actual frequencies, they had a much clearer image of a patient, and this image resulted in greater perceptions of risk. Representations of risk in the form of probabilities are much more benign and don’t conjure up the images that data in the form of frequencies do.

In a different study, researchers asked respondents to determine whether to purchase equipment for use in airport safety in the event of an airliner crash landing. [5] They split the respondents into two groups, telling Group A that the equipment would save 150 lives and telling Group B that the equipment would save 98% of the 150 lives in jeopardy. Which group do you think was more in favor of purchasing the safety equipment? Interestingly, Group B was more strongly in favor of purchasing the equipment. But how could this be? How could they consider saving 98% of 150 lives in jeopardy more convincing than saving all 150 lives?!

Researchers concluded that the respondents in Group A had difficulty assigning meaning to the number 150. Within the context of this scenario, is this number good or bad? For respondents in Group B, however, it proved much easier to assign meaning to the data—98% of something, anything, is clearly very good. It’s almost 100%, falls within clear upper and lower bounds, and is, therefore, very easy to evaluate.

People determine value through the process of comparing things. People do not possess an innate ability that lets them know the value of something. Unless a number of lives saved is explicitly comparable from one scenario to another, it is much easier to evaluate the proportion of lives saved rather than the actual number of lives saved.

Now, this is an interesting finding, because it seems to fly in the face of the findings of the study I discussed immediately before this one. In the mental-patient study, people identified more with the frequency format, while in the airline safety equipment study, people identified more with the probability format. So, what’s going on here? Which format is better?

Well, as is so often the case in UX design, it depends. As designers, we cannot simply say that a frequency format is always best. Instead, we need to do our homework and really understand how people perceive and process data, given the format in which we present the data and the type of problem or scenario we’re asking people to consider and evaluate.

UX Design Considerations

There are some general principles about people’s ability to perceive and comprehend numeric data that can guide UX design. For example, people usually have a harder time understanding probabilities when they are given in the format of percentages rather than frequencies. [6] Let’s consider the following two statements as an example:

• a 30% chance of rain
• a 3 in 10 chance of rain

Which of these do you think people would understand most easily? Research shows that people have an easier time interpreting the second example. This is because it is easy to misinterpret the first example. Some common misinterpretations include the following:

• It will rain in 30% of the area.
• It will rain 30% of the time.
• It will rain on 30% of days similar to this one.

Similar types of confusion can result when doctors talk about medical conditions with patients. If a doctor tells patients that there is a 30% chance of their developing a problem if they engage in a certain activity, some patients would likely interpret this to mean that they would experience that problem 30% of the time when engaging in that activity. However, stating a probability as a frequency—for example, that only 3 of 10 people engaging in the activity would experience this problem at all—makes the distinction clear.

Summing Up

Earlier, I said that, for people to use numeric data effectively, they need to be able to do three things:

• Comprehend it.
• Interpret it—and attach the right meaning to it.
• Act on it.

People use data in decision making only when they can glean meaning from it. They derive meaning through their ability to visualize data or to judge the value of something by making a comparison against a reference point or within the context of upper and lower bounds.

Even though we can’t say people always understand frequencies better than probabilities in percentage formats, we can rely on the consistency of the process people use to derive value and meaning—the process of comparison within the context that we provide.

UX designers can play a pivotal role in driving effective consumer decision making by architecting decision making contexts that enable people to easily derive meaning from numeric data. Remember, the ease with which people can derive meaning dictates the extent to which they will use data. 

References

[1] Bateman, Ian, Sam Dent, Ellen Peters, Paul Slovic, and Chris Starmer. “The Affect Heuristic and the Attractiveness of Simple Gambles.” Journal of Behavior Decision Making, Volume 20. Retrieved May 18, 2011.

[2] Denes-Raj, Veronika, and Seymour Epstein. “Conflict Between Intuitive and Rational Processing: When People Behave Against Their Better Judgment.”PDF Journal of Personality and Social Psychology, Volume 66, 1994. Retrieved May 18, 2011.

[3] Yamagishi, Kimihiko. “When a 12.86% Mortality Is More Dangerous Than 24.14%: Implications for Risk Communication.”PDF Applied Cognitive Psychology, Volume 11, 1997. Retrieved May 18, 2011.

[4] Slovic, Paul, John Monahan, and Donald MacGregor. “Violence Risk Assessment and Risk Communication: The Effects of Using Actual Cases, Providing Instructions, and Employing Probability vs. Frequency Formats.” Law and Human Behavior, Volume 24, 2000. Retrieved May 18, 2011.

[5] Fetherstonhaugh, David, Paul Slovic, Stephen Johnson, and James Friedrich. “Insensitivity to the Value of Human Life: A Study of Psychophysical Numbing.” Journal of Risk and Uncertainty, Volume 14, 1997. Retrieved May 18, 2011.

[6] Gigerenzer, Gerd, and Adrian Edwards. “Simple Tools for Understanding Risks: From Innumeracy to Insight.” British Medical Journal, 2003. Retrieved May 18, 2011.