A Picture’s Worth a Thousand Numbers

Since the 1960s, researchers have explored the trouble humans have understanding probability. New studies by ourselves and others show that the way data are presented has a big impact—in particular, graphic representations and computer simulations can help. In one experiment, we gave 257 economists a simple regression analysis and asked about the odds of various outcomes. Some were shown the data in the form customary in economics journals: the mean, the standard deviation, and so on. They got most of the answers wrong. Others were given a scatterplot, with no analysis. Although some of them complained about not having enough information, most did much better. Probability: A Clearer View Your company is considering a $100 million investment in a new factory. The number crunchers estimate that the plant will generate an annual return of 20% over a 10-year lifespan. But they also say the estimate has a standard deviation of 70%. What are the chances things will go wrong? Stumped? If you run 1,000 simulations of the results and enter them on a scatterplot, the scenario becomes more intuitive. As companies increasingly rely on analytics and Big Data, it’s important to use infographics to present information in ways decision makers can easily understand. Early on, the likelihood of a loss is not trivial. At year one it’s 38%; after three years it’s 19%. By the 10th year the chance of a cumulative loss from plant operations is quite small—0.3%. But the odds that you won’t have recouped your investment are still 8%. In complex problems where graphing is not an option, computer simulations let people “experience” odds by running numerous versions of the underlying statistical process and seeing the results. (Flipping a coin repeatedly is a simple example of a simulation.) We hypothesize that although probability theory is a fairly recent invention, people have been encoding and interpreting sequentially observed “frequency information” for eons—so the human brain has some experience with odds presented in that form. Our research bears the hypothesis out. We gave statistical puzzles to 62 undergraduate students who’d recently taken classes in statistics and 20 adults who were less statistically inclined. In both groups, people were much more likely to give correct answers after running simulations. We believe these results hold great promise for improving statistical understanding in business, government, and other fields. For example, firms deciding whether to buy new equipment and individuals choosing retirement portfolios face considerable risk and uncertainty. Statistical analyses can estimate the risk and aid in decision making—but most of us struggle to make sense of those analyses. Graphs and simulations let people observe potential outcomes and effectively experience the risks, enabling them to make better choices.

A Picture’s Worth a Thousand Numbers

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