No Strength in Numbers

Imagine you thought you were competing in a race against 10 people of similar ability. Would you try your best? What if that number increased to 100? Would you still try your best? Probably not, according to new research published in the journal Psychological Science by Stephen Garcia, Ed.M.'02, and Avishalom Tor. Based on a series of studies, Garcia and Tor found that as the number of competitors (real or perceived) increases, the motivation to compete decreases.

This "N-effect," as they call it, can have a profound impact on education, says Garcia, an assistant professor at the University of Michigan who met Tor, a Harvard Law School graduate, while they were both students. For example, using SAT scores from 2005, they found that the more people there were taking the test at a site, the lower the average SAT score. They wondered, Were students preoccupied by the sheer number of other test takers they were "competing" against or by distractions that might occur in a larger space -- more noises, for example? Because they were analyzing data at the state level, not detailed data on each individual, they also had to take into consideration other factors that could explain high or low scores such as population density and parental education. They also analyzed results of the Cognitive Reflection Test, which is correlated to the SAT, from a homogenous sample of University of Michigan students. The same pattern emerged: the more students that showed up to take the test, the lower the average score for the session.

Still, says Garcia, these "correlation-based studies" have limitations.

"That's why we moved to another experiment. We recruited 74 undergraduates at the University of Michigan to take a short, easy quiz. We told them that if they finished in the top 20 percent in terms of speed, they would get $5," he says. The quiz wasn't a test of their knowledge -- questions were intentionally designed to allow everyone to easily answer all of them (the name of the president of the college, for example). Students took the test by themselves in a room. Some were told they were competing against 10 others; some, against 100. Again, like with the SAT results, Garcia and Tor found that the number of competitors -- this time perceived -- affected the outcome.

"The people who thought they were competing in a pool of 10 finished faster than those who thought they were competing in a pool of 100," Garcia says. "This showed us that the actual presence of others isn't necessary to affect the results."

To further prove their point, Garcia and Tor asked another group of undergraduates to imagine they were competing in two five-kilometer races: one with 50 runners of similar abilities, another with 500. On a scale of one to seven, they had to say to what extent they would run faster than normal. Participants also answered a series of questions related to social comparison theory -- how much people compare themselves to others.

"We found that people running in a race of 50 would try much harder, the fastest in their lives," Garcia says. This was especially true of people who scored high on the social comparison questions. "Those who scored low, it didn't matter if they raced against 50 or 500 -- they tried the same. Social comparison is a necessary precondition for the N-effect."

Garcia says educators and education policymakers could use the results of their study in several ways. First, he says, it could help inform the class-size debate.

"Traditionally the debate has focused on how much attention teachers can give to students," he says. "The N-effect suggests that the motivation to do well is affected by the number of students in a classroom. Motivation goes down as the number of students goes up. Students impact each other, regardless of the teacher's attention. Educators could, therefore, pay more attention to class design and the number of students per class."

Second, he says the study could impact the debate about teacher pay being linked to student performance.

"This research suggests that teachers with larger class sizes are more likely to have lower test scores," he says.

Last, there are implications for fair testing practices, he says, especially on such important tests as the SAT, which is used by many colleges and universities as an admissions tool.

"Testing providers do their best, but the discovery of the N-effect suggests that the number of test takers affects results," he says. "This really could be a big fairness issue."

Go to www.sitemaker.umich.edu/stephen.garcia/files/n-effect.pdf to download the study.