OR many education advocates, the arts are a panacea: They supposedly increase test scores, generate social responsibility and turn around failing schools. Most of the supporting evidence, though, does little more than establish correlations between exposure to the arts and certain outcomes. Research that demonstrates a causal relationship has been virtually nonexistent.

A few years ago, however, we had a rare opportunity to explore such relationships when the Crystal Bridges Museum of American Art opened in Bentonville, Ark. Through a large-scale, random-assignment study of school tours to the museum, we were able to determine that strong causal relationships do in fact exist between arts education and a range of desirable outcomes.

Students who, by lottery, were selected to visit the museum on a field trip demonstrated stronger critical thinking skills, displayed higher levels of social tolerance, exhibited greater historical empathy and developed a taste for art museums and cultural institutions.

Crystal Bridges, which opened in November 2011, was founded by Alice Walton, the daughter of Sam Walton, the founder of Walmart. It is impressive, with 50,000 square feet of gallery space and an endowment of more than $800 million.

Thanks to a generous private gift, the museum has a program that allows school groups to visit at no cost to students or schools.

Before the opening, we were contacted by the museum’s education department. They recognized that the opening of a major museum in an area that had never had one before was an unusual event that ought to be studied. But they also had a problem. Because the school tours were being offered free, in an area where most children had very little prior exposure to cultural institutions, demand for visits far exceeded available slots. In the first year alone, the museum received applications from 525 school groups requesting tours for more than 38,000 students.

As social scientists, we knew exactly how to solve this problem. We partnered with the museum and conducted a lottery to fill the available slots. By randomly assigning school tours, we were able to allocate spots fairly. Doing so also created a natural experiment to study the effects of museum visits on students, the results of which we published in the journals Education Next and Educational Researcher.

Over the course of the following year, nearly 11,000 students and almost 500