Methodological issues with the “average” American wedding costing $27,000

Recent news reports suggest the average American wedding costs $27,000. But, there may be some important methodological issues with this figure: selection bias and using an average rather than a median.

The first problem with the figure is what statisticians call selection bias. One of the most extensive surveys, and perhaps the most widely cited, is the “Real Weddings Study” conducted each year by TheKnot.com and WeddingChannel.com. (It’s the sole source for the Reuters and CNN Money stories, among others.) They survey some 20,000 brides per annum, an impressive figure. But all of them are drawn from the sites’ own online membership, surely a more gung-ho group than the brides who don’t sign up for wedding websites, let alone those who lack regular Internet access. Similarly, Brides magazine’s “American Wedding Study” draws solely from that glossy Condé Nast publication’s subscribers and website visitors. So before they do a single calculation, the big wedding studies have excluded the poorest and the most low-key couples from their samples. This isn’t intentional, but it skews the results nonetheless.

But an even bigger problem with the average wedding cost is right there in the phrase itself: the word “average.” You calculate an average, also known as a mean, by adding up all the figures in your sample and dividing by the number of respondents. So if you have 99 couples who spend $10,000 apiece, and just one ultra-wealthy couple splashes $1 million on a lavish Big Sur affair, your average wedding cost is almost $20,000—even though virtually everyone spent far less than that. What you want, if you’re trying to get an idea of what the typical couple spends, is not the average but the median. That’s the amount spent by the couple that’s right smack in the middle of all couples in terms of its spending. In the example above, the median is $10,000—a much better yardstick for any normal couple trying to figure out what they might need to spend.

Apologies to those for whom this is basic knowledge, but the distinction apparently eludes not only the media but some of the people responsible for the surveys. I asked Rebecca Dolgin, editor in chief of TheKnot.com, via email why the Real Weddings Study publishes the average cost but never the median. She began by making a valid point, which is that the study is not intended to give couples a barometer for how much they should spend but rather to give the industry a sense of how much couples are spending. More on that in a moment. But then she added, “If the average cost in a given area is, let’s say, $35,000, that’s just it—an average. Half of couples spend less than the average and half spend more.” No, no, no. Half of couples spend less than the median and half spend more.

When I pressed TheKnot.com on why they don’t just publish both figures, they told me they didn’t want to confuse people. To their credit, they did disclose the figure to me when I asked, but this number gets very little attention. Are you ready? In 2012, when the average wedding cost was $27,427, the median was $18,086. In 2011, when the average was $27,021, the median was $16,886. In Manhattan, where the widely reported average is $76,687, the median is $55,104. And in Alaska, where the average is $15,504, the median is a mere $8,440. In all cases, the proportion of couples who spent the “average” or more was actually a minority. And remember, we’re still talking only about the subset of couples who sign up for wedding websites and respond to their online surveys. The actual median is probably even lower.

These are common issues with figures reported in the media. Indeed, these are two questions the average reader should ask when seeing a statistic like the average cost of the wedding:

1. How was the data collected? If this journalist is correct about these wedding cost studies, then this data is likely very skewed. What we would want to see is a more representative sample of weddings rather than having subscribers or readers volunteer how much their wedding cost.

2. What statistic is reported? Confusing the mean and median is a big program and pops up with issues as varied as the average vs. median college debtthe average vs. median credit card debt, and the average vs. median square footage of new homes. This journalist is correct to point out that the media should know better and shouldn’t get the two confused. However, reporting a higher average with skewed data tends to make the number more sensationalistic. It also wouldn’t hurt to have more media consumers know the difference and adjust accordingly.

It sounds like the median wedding cost would likely be significantly lower than the $27,000 bandied about in the media if some basic methodological questions were asked.

Assessing “The Return of McMansions” in the NYT

Following up on the same data behind the CNN story on the McMansion comeback, the NYT looks more closely at the characteristics of new houses in 2012. Here is my summary:

-Housing starts were still down in 2012. Looking at the graph with housing start data since 1973 shows that the last few years have been quite different.

-The homes built in 2012 were bigger: the highest median square footage ever of 2,306 square feet, 41% of the houses were four or more bedrooms (a new record), and 30% of new houses had 3 or more bathrooms (also a new record).

My thoughts on this data:

1. This is not a big surprise. While housing starts are way down, wealthier Americans and others have still been able to buy large new homes. Again, Toll Brothers is doing just fine. On the other hand, the lower ends of the housing market are not doing well.

2. It is interesting again for people to pick up on the highest-ever median square footage for new houses. For years, journalists and others have looked at the average square footage which is bit down from its high several years ago. Perhaps the median is now alluring because it is at its highest point and therefore can be linked to McMansions and American excess?

3. More houses have more bedrooms and yet the average family size in the United States has decreased in recent decades and more Americans are now living alone. So what are these bedrooms being used for?

 

CNN says “McMansions are making a comeback” but the data is limited

CNN reports that McMansions just may be on the way back:

During the past three years, the average size of new homes has grown significantly, according to a Census Bureau report released Monday. In 2012, the median home in the U.S. hit an all-time record of 2,306 square feet, up 8% from 2009.

During the recession, Americans downsized and the average new home shrunk in size by 6% over two years to 2,135 square feet. At the time, many industry experts said the days of the McMansion were over.

The shrinkage was supposed to indicate that a new era had begun, with young buyers seeking to live closer to urban cores and settling for smaller places and baby boomers downsizing after their kids had flown the nest.

But it wasn’t that consumers wanted less space, many just couldn’t afford more, said Jeffry Roos, a regional president for home builder Lennar. And now that the economy is improving, they’re demanding bigger homes again, he said.

This is what I suspected might happen: once the housing market picked up again, some Americans would go back to buying bigger houses. But, this article has a few problems as it relies on (1) the median home size and (2) talking to several large builders.

Regarding home size: the figures cited more often is the average home size. The average size for new houses went from roughly 900 square feet in 1950 to nearly 2,500 in the mid-2000s. The median home size might be more accurate as the extra big homes can’t skew the data as much but the average is used more often. Also, the median hasn’t changed all that much in the last few years – this is only a difference of 150 square feet, a 12×12 room. Why can’t we see figure about the number of big homes that have or have not been built rather than relying on these overall figures that are a snapshot of a varied housing industry?

Relying on just a few large builders also does not reveal the big picture. The builders cited, particularly Toll Brothers, are big players but the housing market has a lot of different builders and developers. Overall, how are lots of different builders feeling about big houses? Are they actually building these bigger houses? What do real estate experts say? The news for Toll Brothers has looked good recently but there is more to the big house market than just Toll Brothers.

This seems like an article that would benefit from better data and also may not really be able to be written until some more time has passed and the trend is more clear. In the meantime, simply invoking the term McMansion and discussing a possible trend is apparently enough…

UPDATE 6/5/13: As the CNN story is repeated across the web, there is some confusion. For example, look at how this retelling mixes the idea of an average or median:

A new Census Bureau report says the average size of a new home has grown eight percent in the last three years, up to a record 2,300 sq. ft. in 2012…

According to the National Association of Homebuilders, buyers prefer a median home size of just over 2,200 feet, in line with the Census average.

Two different figures for the “middle” size mean two different things…

The problem with using averages as illustrated by the average salaries of NBA players

In negotiations between NBA owners and players, the topic of the “average player salary” has come up. This discussion illustrates some of the issues involved with  using averages and medians:

Here is the “average player salary” for each of the major U.S. professional team sports, based on a variety of sources using the most recent data available:

NBA: $5.15 million (2010-11)

MLB: $3.34 million (2010)

NHL: $2.4 million (2010-11)

NFL: $1.9 million (2010)

From the public’s view, these numbers are high in all four sports. But players and agents argue that these averages obscure important distinctions including the value of certain positions over others (the quarterback in the NFL versus the punter) and the size of the roster (fewer NBA players, more NFL players).

One common solution to problems with averages is to instead use a median. Here is how this might change the discussion in the NBA:

“It’s the median salary that’s more important,” NBA agent Bill Duffy said. “Look at the Miami Heat as an analogy here: You’ve got three guys making $17 million and probably six guys making $1.2 [million]. So that’s a little misguided, that average salary.”…

It is not unlike, Duffy said, news stories that cite the “average” U.S. household income as opposed to the median. The latter figure, according to the most recent U.S. census, was $50,233. If you were to average in the dollar amounts pulled down by Wall Street bankers, Ivy League lawyers, certain public-union employees and yes, professional athletes, that number would jump considerably.

Curiously, neither the NBA nor the NBPA seems to make much use of a median player salary.

“We use [average] because it’s the most commonly used measure and best reflects the amount of compensation that the NBA provides to players across the league,” an NBA spokesman said this week. “In addition, it’s the measure that both we and the union agreed upon in the CBA.”

In the NFL, the median salary is approximately $770,000 — about 40 percent of the average.

In the NBA, using USA Today salary figures for the 2009-10 season, the estimated median salary was about $2.33 million. That’s still about 46 times what the median U.S. household earns, but it is less than half what the max-salary-bloated “average” is.

What happens in these sports is this: a small number of star athletes make huge amounts of money, pulling the average for all athletes up. If you use the median instead, where 50% of the players make more and 50% more make less, it suggests that more of the athletes in each sport make less. Particularly in the NFL which has bigger rosters, the difference between the average and the median shows that many players make very little.

It is interesting that the NBA spokesman said the two sides had agreed in their Collective Bargaining Agreement that they would use the average salary figure. Was this really a point of contention negotiations or did no one really think about the consequences? What was the thinking behind this for the players? If the union was focused on helping all of their members, perhaps they would focus on the median, suggesting that they are strongest when all of their members are well taken care of. This lower figure might also look more palatable to the public though it is unclear whether public perceptions have any influence on such negotiations. However, if the union was more interested in making sure that individual athletes could receive the biggest possible payouts because of their athletic exploits, then perhaps the average is better.

Two takeaway points:

1. Averages and medians are both measures of central tendency but they are open to different interpretations. People need to be clear about which they are using and which interpretation their number interprets.

2. It will be interesting to see if the new CBA is based on average or median salaries.