Imagine that you see two people in the distance walking alongside each other down a busy sidewalk. Maybe they are a couple. Maybe they just happen to be heading in the same direction. In a crowd of people on a city street, it’s hard to tell.

That same challenge arises when researchers look at possible links among social, economic and demographic trends. Two trends are heading in the same direction, but are they related? Correlation, the statisticians frequently warn, is no guarantee of causation.

There is wide interest by researchers and journalists in finding data from the Census Bureau and other sources that could illustrate the impacts of the Great Recession on American life. This posting recounts a recent debate over the strength of potential links between the recent decline in marriage rates and the national economic downturn.

When the Census Bureau released its 2009 American Community Survey estimates Sept. 29, many news accounts focused on showing how the numbers illustrated the impact of the Great Recession. A number of news stories — including those in the New York Times, Wall Street Journal, USA Today, Bloomberg news service, Associated Press and AOL news –picked up on findings that for the first time, more 25-to-34-year-olds have never married than are married. Among those ages 18 and older, 52% are married, the lowest proportion since the government began collecting data on this measure more than a century ago.

The numbers they cited were included in an analysis of ACS and other recent census data from the respected Population Reference Bureau in Washington. The PRB analysis noted that marriage rates among young people have been dropping for years, but the decline has accelerated since the recession began. “The data suggest that more young couples are delaying marriage or foregoing matrimony altogether, likely as an adaptive response to the economic downturn and decline in the housing market,” wrote Mark Mather and Diana Lavery. PRB’s analysis, however, added additional qualifications, noting that state-level patterns were murkier; rising unemployment was associated with lower marriage rates in some states but not others. (Sociologist Philip N. Cohen of the University of North Carolina also picked up on the idea that the recession “seems to be hurrying” along a decline in marriage.)

As PRB did, many journalists qualified their conclusions with phrases such as “may have had an impact” or “trend appeared to accelerate.” Their headlines, as is typical in journalism, were more definitive: “Recession Spurs Young in US to Forgo or Delay Marriage,” read one. “Saying No to ‘I Do,’ With the Economy in Mind,” said another.

A few days later, Census Director Robert Groves, who had a long career as a social scientist before taking over the agency in 2009, contributed his thoughts. On his director’s blog, he noted that some news coverage had stated that the declining number of marriages in the U.S. was directly related to the economic downturn. That inference may not be valid, Groves said, and more information may be needed to make the assertion.

Many factors can affect the number of marriages, he said, and pointed out, as did the PRB report, that the share of Americans who are currently married has been dropping for decades. (So did this blog posting on the Cincinnati Enquirer website, written by Janet Harrah of Northern Kentucky University. Its title: “Statistics: A Cautionary Tale.”)

“The impact of an external event, such as an economic recession, can’t easily be teased out of the change over time,” Groves wrote. “It would be useful to such inference to see whether persons considering marriage before and after the recession were making different decisions. It would be useful to know whether those couples most affected by the recession (e.g., losing a job, having a home foreclosed), were more prone to put off marriage relative to those unaffected by the recession. But these estimates were not part of the ACS report.

Statistical estimates are critical to understanding our nation, who we are and how we live. We just need to take care that we understand what they can and cannot tell us about our country.”

Economist Justin Wolfers added his views last week, with an op-ed in The New York Times, a posting on the paper’s Freakonomics blog and an essay on the Brookings Institution website.

He wrote: “You’ve probably heard the latest marriage narrative: With the recession upon us, young lovers can’t afford to marry. As appealing as this story is, it has one problem: It’s not true.” There is no systematic pattern to marriage rates and the economy, he argues: “In fact, the marriage rate appears amazingly insensitive to the business cycle.”

Wolfers employed different statistics than PRB did: He looked at the number of new marriage certificates per 1,000 people for different time periods, including during economic recessions. He argued that the decline in marriage among 25-to-34-year-olds is due more to another trend-Americans are getting married for the first time at older ages than they once did-than to the economy. There is a rise in cohabitation that could well be related to the Great Recession, he said, because couples are trying to save money by living together. Many of them, he added, eventually will marry.

Find more analyses of Census-related data and happenings at All Things Census.