The Impact Number Formats Have on Judgment and Decision Making

Decision Architecture

Designing for decision making

A column by Colleen Roller
June 7, 2011

People must often make important decisions that involve the ability to interpret and act on numeric data. The financial services and healthcare industries, for example, commonly provide consumers with significant amounts of numeric information, so they can make informed decisions regarding their finances and health.

There are a variety of ways in which we can present numeric data to consumers—for example, as frequencies, percentages, decimals, or fractions. Does it matter how we display numeric data? Do number formats affect decision outcomes or the ways in which people interpret or use numeric data? These questions are worth considering, especially because so many critical decisions—from those involving personal finances to those about medical treatments that could have serious, life-impacting consequences—depend on people’s ability to use numeric data to make appropriate decisions.

In this column, I want to take a look at several research studies that have revealed how what kind of data we display and how we display that data influences people’s judgments and decisions. These research findings can help us understand how to better present and format numeric data to help consumers make informed decisions.

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Using Context and Comparison to Enable Meaning

Let’s begin by considering a study in which researchers asked two groups of people to rate the attractiveness of a simple gamble. They asked Group A to consider a gamble in which they were given a 7/36 chance of winning $9. They asked Group B to consider a similar gamble, but added the potential for a small loss—that is, Group B’s gamble gave them a 7/36 chance of winning $9 or, conversely, a 29/36 chance of losing 5¢. Which group do you think rated their option as most attractive?

Although Group A’s gamble was clearly better than Group B’s, people actually rated the gamble with some potential for a small loss as more attractive. The mean response to the first gamble was 9.4, while in the gamble that added a chance of a small loss, the mean was 14.9. [1]

Why would the adding the potential for a small loss make such a difference? Researchers concluded that, in the gamble with no potential for loss, people focused primarily on their probability of winning rather than on the possible monetary outcome. This is because probability is easy to assess—there are known upper and lower bounds that provide context, and in the example of this gamble, the probability of winning is relatively unattractive—only 7 out of 36 chances of winning.

The $9 monetary value of the gamble is harder to assess. Is winning $9 good or bad? Attractive or not? Adding the chance of a small loss puts the $9 payoff in perspective and gives it meaning. The value of $9 was much clearer and more positive in the presence of the 5-cent loss. The combination of a possible $9 gain versus a 5-cent loss is an attractive win/lose ratio—that is, it offers a good-value win versus a very small loss.

Remember, as I’ve described in my previous columns, that people determine value through a process of comparing things. It’s not so much that people can’t comprehend the value of $9. The real issue is: what does $9 really mean in the context of this gamble? Is a $9 payoff good or bad? Without the context of a reference point—in this case, a 5-cent loss—it’s hard to judge the worth of the $9.

Numeric Data and Decision Making

Research shows that the ease with which people can derive meaning dictates the extent to which they will use data. 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 must be able to successfully comprehend and attach meaning to data before they can act on it. UX designers can play a critical role in enabling this process.

Rote Frequencies and Decision Making

Let’s take a look at some additional research that can help us understand the nuances of how data format affects judgment and decision making.

In one study, researchers gave a group of people a chance to win a prize by drawing a red bean from a bowl containing red and white beans. [2] There were two bowls from which they could choose. In one bowl, there were 100 beans, 7 of which were red. In the other bowl, there were 10 beans, one of which was red. A significant number of people wanted to choose from one bowl rather than the other. Can you guess which bowl was most popular?

Although they actually had a better probability of winning if they chose from the bowl with fewer beans, many people preferred to choose from the bowl with more beans. Why? Because the image of seven winning beans was more attractive than the image of one winning bean. The larger bowl looked more inviting because it contained more red beans and seemed to give people more chances of winning.

Notice what people are doing here. They are focusing only on the number of winning beans and ignoring the rest of the context—the remaining white beans in each bowl—as they think about which bowl from which to choose. Gut—which makes an immediate decision prior to Head’s weighing in—strongly influences this mental shortcut. Remember, from my previous columns, that Gut is attuned to basic elements of contrast—such as the difference between big and small or light and dark.

Another study found a similar effect when researchers asked people to judge which disease is more dangerous—one that kills 1,286 out of every 10,000 people or one that kills 24 out of every 100 people. [3] Can you predict how most people responded? Results of the study showed that the degree of perceived risk varied according to the number of deaths researchers presented—irrespective of the total number of possible deaths.

One practical application of this finding is that, since many people judge the level of risk according to rote frequency, the format in which you present numbers can affect people’s perception of the level of risk. In general, higher rote frequencies result in higher perceived risk and vice versa.

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. 


[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.

VP, Senior UX Researcher at Bank of America Merrill Lynch

Boston, Massachusetts, USA


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