Tag Archives: statistics

Untangling the effects of TV watching on mortality

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Interpreting the results of studies can be difficult, particularly if one confuses a correlation (indicating some relationship between two variables) and a direct causal relationship (where one variable causes another). This usually is translated into the common phrase “correlation, not causation” which is illustrated in this example from Entertainment Weekly:

Researchers in Australia are reporting that, on average, every hour spent watching television after the age of 25 decreases the amount you live by 22 minutes.

“As a rule, the more time we spend watching TV, the more time we spend eating mindlessly in front of the TV, and the less time we spend being physically active,” explained Dr. David L. Katz, director of the Prevention Research Center at Yale University School of Medicine to HealthDay.com. “More eating and less physical activity, in turn, mean greater risk for obesity, and the chronic diseases it tends to anticipate, notably diabetes, heart disease and cancer.”

Before you throw your soul-sucking flat screen out the window, here’s a key thing to remember:

TVs are not like the year-draining torture machine in The Princess Bride. This study measures a casual lifestyle correlation — people who watch a lot of TV, on average, die younger than those who do not.

This seems to make sense – it is not TV watching that is the real issue but rather sitting around a lot, which is related to TV watching. This was echoed in the HealthDay story the EW post refers to:

But other experts cautioned that the study did not show that TV watching caused people to die sooner, only that there was an association between watching lots of TV and a shorter lifespan.

But I wonder if this is more of a conceptual issue that an analysis issue on the part of the original researchers. While I can’t access the original article, here is part of the abstract that sheds light on the issue:

Methods The authors constructed a life table model that incorporates a previously reported mortality risk associated with TV time. Data were from the Australian Bureau of Statistics and the Australian Diabetes, Obesity and Lifestyle Study, a national population-based observational survey that started in 1999–2000. The authors modelled impacts of changes in population average TV viewing time on life expectancy at birth.

Results The amount of TV viewed in Australia in 2008 reduced life expectancy at birth by 1.8 years (95% uncertainty interval (UI): 8.4 days to 3.7 years) for men and 1.5 years (95% UI: 6.8 days to 3.1 years) for women. Compared with persons who watch no TV, those who spend a lifetime average of 6 h/day watching TV can expect to live 4.8 years (95% UI: 11 days to 10.4 years) less. On average, every single hour of TV viewed after the age of 25 reduces the viewer’s life expectancy by 21.8 (95% UI: 0.3–44.7) min. This study is limited by the low precision with which the relationship between TV viewing time and mortality is currently known.

Conclusions TV viewing time may be associated with a loss of life that is comparable to other major chronic disease risk factors such as physical inactivity and obesity.

Some key parts of this:

1. This was done using life table models, not correlations. Without seeing the full article, it is hard to know exactly what the researchers did. Did they simply calculate a life table (see an example in 7.2 here) or did they run a model that included other independent variables?

2. Their confidence intervals are really wide. For example, the amount of TV watched in 2008 could only shorten someone’s life by 8.7 days, hardly a substantively significant amount over the course of a lifetime. Watching 6 hours a day on average (compared to those who watch no TV), could live just 11 minute shorter lives.

3. The abstract suggests there is “low precision” because this link hasn’t been studied before. If this is true, then we need a lot more science on the topic and more data. This article, then, becomes an opening or early study on the topic and is not the “definitive” study.

4. The conclusion section says “may be associated with a loss of life that is comparable to other major chronic disease risk factors such as physical inactivity and obesity.” The key word here is “may.” This might simply be an academic qualification but it is an important distinction between saying “proved” (how the public might want to interpret it).

Here is my guess at what happened: media reports (or perhaps even a press release) about the study were a lot more strident about these results than the researchers themselves. In fact, here is a piece from the HealthDay piece that suggests this may be the case:

Researchers in Australia found that people who averaged six hours a day of TV lived, on average, nearly five years less than people who watched no TV.

The emphasis here is on the average, not necessarily the confidence interval. This would be like reporting poll results that say a candidate leads by 6 over an opponent but forgetting to mention that the margin of error (a confidence interval) is 5.9.

What the HealthDay report should include: comments from the researchers themselves explaining the work. Interestingly, the story quickly suggests that other researchers say there are other factors at work but we never hear from the original researchers outside of a few pieces lifted from the study. Without the proper context, a study can become a “shock headline” used by media sites to drive traffic.

I do have to ask: does Entertainment Weekly have a vested interest in debunking a study like this since they are in the business of reviewing television shows and channels?

The “value of estimating”

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Here is another way to help students develop their mathematical skills: learn how to estimate.

Quick, take a guess: how tall is an eight-story building? How many people can be transported per hour on a set of train tracks in France? How many barrels of oil does the U.S. import each year?

Maybe you gave these questions your best shot – or maybe you skimmed right over them, certain that such back-of-the-napkin conjecture wasn’t worth your time. If you fall into the second, just-Google-it group, you may want to reconsider, especially if you’re a parent. According to researchers who study the science of learning, estimation is the essential foundation for more advanced math skills. It’s also crucial for the kind of abstract thinking that children need to do to get good grades in school and, when they’re older, jobs in a knowledge-based economy.

Parents can foster their kids’ guessing acumen by getting them to make everyday predictions, like how much all the items in the grocery cart will cost. Schools, too, should be giving more attention to the ability to estimate. Too many math textbooks “teach how to solve exactly stated problems exactly, whereas life often hands us partly defined problems needing only moderately accurate solutions,” says Sanjoy Mahajan, an associate professor of applied science and engineering at Olin College…

Sharpen kids’ logic enough and maybe some day they’ll dazzle people at cocktail parties (or TED talks) the way Mahajan does with his ballpark calculations. His answers to the questions at the top of this story: 80 ft., 30,000 passengers and 4 billion barrels. To come up with these, he guessed at a lot of things. For instance, for the number of barrels of oil the U.S. imports, he made assumptions about the number of cars in the U.S., the number of miles driven per car per year and average gas mileage to arrive at the number of gallons used per year. Then he estimated how many gallons are in a barrel. He also assumed that imported oil is used for transportation and domestic for everything else. The official tally for U.S. imports in 2010 was 4,304,533,000 barrels. Mahajan’s 4 billion isn’t perfect, but it’s close enough to be useful – and most of the time, that’s what counts.

It sounds like estimation helps with problem solving skills and taking known or guessed at quantities to develop reasonable answers. I tried this question about the barrels of oil with my statistics class today and we had one guess of 4 billion barrels (among a wide range of other answers). This also suggests that there is some room for creativity within math; it isn’t all about formulas but rather takes some thinking.

This reminds me that Joel Best says something similar in one of his books: being able to quickly estimate some big figures is a useful skill in a society where statistics carry a lot of weight. But to do some of this, do people have to have some basic figures in mind such as the total population of the United States (US Census population clock: over 312 million)? Is this a commonly known figure?

The article also suggests ways to take big numbers and break them down into manageable and understandable figures. Take, for example, the national debt of the United States is over 15 trillion dollars, a figure that is perhaps impossible to comprehend. But you could break it down in a couple of ways. The debt is slightly over $48k per citizen, roughly $192k per family of four. Or you could compare the debt to the yearly GDP.

Politicial scientist uses social science skills to dissect soccer statistics

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Social scientists do venture out of the ivory tower. Here is an example of a political scientist (who also teaches political sociology and has reviewed for several sociology journals) who uses his analytical skills to examine soccer numbers:

Chris Anderson found himself keeping goal for a West German fourth-division club at 17. He managed to hold on to the starting position for a couple of seasons, earning a few Deutsche Marks and watching the game from up close. Today he’s an award-winning professor at Cornell University, where he teaches political economy and political sociology. He consults with clubs about football numbers and his writings appear on his Soccer By The Numbers blog and other football publications, including the New York Times’ Goal blog…

I am primarily an academic who just happens to know a little about both soccer and about statistics. I was born and raised in Europe, so soccer was everywhere when I was growing up. Not to date myself, but the 1974 World Cup in Germany was a formative experience for me. That’s when I started playing. Eventually, I quit and became an academic, but fortunately, the analytical tools I use in my “day job” as a social scientist can easily be applied to soccer data. I read Soccernomics (by Simon Kuper and Stefan Szymanski) and was hooked. So last year during the World Cup, I started playing around with some data and writing about them on soccerbythenumbers.com. Since then, it’s taken on a life of its own. Together with a colleague from another university, I am currently in the process of writing a book about the game using statistical evidence.

It is sabermetrics for soccer! It would be very interesting to hear whether Anderson uses similar techniques in his political science and soccer work and how the soccer works help him keep up on statistical analysis.

A bonus: since Anderson has “been sworn to secrecy” regarding whether he has done detailed analyses for specific teams, we can assume that statistical skills can also lead to getting paid by a sports team.

Cities ranked by the “Trick or Treat Index”

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Richard Florida has put some of his data to use to answer an important question: what are the best cities in the united States for trick or treating on Halloween?

According to National Retail Federation projections, Americans will spend $6.86 billion on Halloween this year, up from $3.3 billion in 2005 when a lot fewer of us were out of work. But even as Halloween edges up on Christmas as a shopping opportunity, the trick-or-treating experience is a lot less universal than it was. In some towns, you see hardly any unsupervised trick-or-treaters after dark; in other places—Brooklyn Heights or my neighborhood in Toronto leap to mind—there are more kids than you can imagine.

Herewith the 2011 edition of the Trick-or-Treater Index developed with the ever-able number-crunching of my Martin Prosperity Institute colleague, Charlotta Mellander. The 2011 Index is based on the following five metrics: the share of children aged 5 to 14; median household income (figuring the haul will be better in more affluent metros), population density, walkability (measured as the percentage of people who walk or bike to work) and creative spirit (which we measured as the percentage of artists, designers, and other cultural creatives). The data are from the American Community Survey and cover all U.S. metro areas, both their cores and suburbs…

As for the top ranking metros, Bridgeport-Stamford-Norwalk, Connecticut, comes in first again this year. Greater New York has moved up to second place, followed by Chicago, greater Washington, D.C., and the twin cities of Minneapolis-St. Paul. Los Angeles, last year’s runner-up, has dropped to 7th place. Big metros dominate the top spots, but Lancaster, Pennsylvania, has moved all the way up from 16th last year to 6th on our 2011 rankings. And college towns like Ann Arbor, Michigan, Boulder, Colorado, and New Haven, Connecticut, also rank among the top 25.

This reminds me of another recent odd use of data that ranked the luckiest cities. So people with more money, who are more creative, and live in more walkable areas necessarily give more or better candy? Might they also be the people who are more likely to give substitutes to candy? Could this also be related to health measures, like obesity or life expectancy? This seems like opportunistic, atheoretical data mining meant to get a few page clicks (like me).

And since there are probably few people who would go to a whole new metropolitan area just to get candy, wouldn’t this be a better analysis if it was at a zip code, community, or census block level?

More $1 million lottery winners each year than NBA players since 1990 that have career earnings over $1 million

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I’ve written before about using the average vs. the median salary in the NBA lockout discussions and here is some more fuel to add to the fire: there are more $1 million lottery winners each year than NBA players who since 1990 have had career earnings of more than $1 million.

I want to call foul on the mainstream media. As I mentioned, a majority of the players in the league make less than $2 million, and yet people like Stephen A. Smith throw around that $5 million figure as gospel. We keep hearing the NBA lockout being described as “millionaires versus billionaires”. But most NBA players won’t become big earners like Kobe and LeBron. Here’s a fun breakdown:

Since the 1990-1991 season 1461 players have entered the NBA and of those:

  • 490 — or 33% — never earned $1 million in career earnings*
  • and that means… 971 have earned at least $1 million in career earnings*
  • 752 have averaged a salary of at least $1 million per year*
  • 643 have earned at least $5 million in career earnings*
  • 165 averaged a salary of at least $5 million per year*

As we can see, less than half of all NBA players in the last 20 years — the period of time where NBA salaries have been at their highest — have hit that $5 million mark over their entire careers. Just over one third — 33% — of all NBA players in the last 20 years have not even hit the $1 million mark in career earnings. And these numbers have been adjusted for inflation!

Here’s a fun comparison: on average, 1600 people win a lottery of at least $1 million every year! That’s right; the lottery has produced almost twice as many millionaires in the last year as the NBA has in the last twenty years!  The popular perception is that once a player enters the NBA they will earn millions and millions of dollars. The truth is that many players don’t hit that high mark.

Both events, winning the big lottery jackpot and becoming a NBA player, are statistically unlikely. However, I suspect that most Americans would say that winning the lottery is much more unlikely. But this blog post points out that even when players do make it to the NBA, a third don’t rake in the big career earnings associated with professional athletes (measured here as $1 million).

This would make for an interesting discussion starter for any professional athlete’s union: should the union be more concerned with allowing a smaller percentage of the athletes maximize their salaries or be more interested in guaranteeing a baseline for the majority of the league that are not stars?

The lottery figures themselves are interesting:

According to the TLC television show, “The Lottery Changed My Life,” more than 1600 new lottery millionaires are created each year. That doesn’t include people that have won jackpots of, say, $100,000 because than the number would be much higher. Still, 1600 is quite a high number.

If 1600 win at least a million in the lotto every year, it means that there are more than 130 each month, more than 30 each week, and more than 4 each day. That’s a lot of winners.

It would be interesting to see more documentation on this.

How to rank the luckiest cities in the United States

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Perhaps we have taken these rankings lists too far: Men’s Health has ranked the luckiest cities in the United States.

Luck is like that dark matter stuff scientists have spent billions of dollars trying to find with the Large Hadron Collider—a powerful presence that people surmise exists but no one has actually seen. The difference is that we found luck. Using statistics instead of protons, we pinpointed the location of a large supply in, of all places, San Diego.

Wondering how Vegas didn’t hit this jackpot? Here’s our definition of good luck: the most winners of Powerball, Mega Millions, and Publishers Clearing House sweepstakes; most hole-in-ones (PGA); fewest lightning strikes (including the fatal kind) and deaths from falling objects (Vaisala Inc., National Climatic Data Center, CDC); and least money lost on lottery tickets and race betting (Bureau of Labor Statistics).

San Diego is number one on the list with Baltimore, Phoenix, Wilmington (Delaware), and Richmond rounding out the top five. Chicago is #36. The bottom five: Sioux Falls, Memphis, Jackson (Mississippi), Tampa, and Charleston (West Virginia).

What I like about this is that they are straightforward with what factors went into the rankings (though they might have been weighted). These are what we might consider “very rare” and cultural conditioned lucky events. The lottery is perhaps the poster child for this. If someone wins more than once, some suspicions might surface (see a story about a four-time Texas winner here). What about lesser luck, such as avoiding a car accident at the last minute or local sports teams coming up with miraculous plays at the end of a game or avoiding natural disasters? Such things would be much more difficult to measure and it might always be an open statistical question of whether strange occurrences could be explained by some other unmeasured or unknown factor.

Should anyone move to the luckier cities to really improve their chances? No, the statistical odds of any of these things happening is still quite small. In fact, it would be interesting to see how much really separates the luckiest cities from the unluckiest – are we talking a difference of 1 in a million? Ten in a million?

In the end, I think these rankings don’t really tell us much about anything. People shouldn’t use them as a guide and measuring luck is fraught with difficulty. Take the lottery winnings: could this simply reflect the fact that people in certain cities buy more tickets or their states have bigger lottery jackpots which encourages more participation? This is a story that uses real numbers to make a nebulous point in order to gain website clicks (guilty as charged) and sell magazines.

Drop in US homeownership rate the greatest since the Great Depression

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The title of this post is what the headline for this AP story should say – instead, the AP headline is “Census: Housing bust worst since Great Depression.” The problem with the headline is this: do people know what a “housing bust” is? Does this mean that the American housing market is in the worst shape that it has been since the Great Depression? Is the homeownership rate or are housing values at the same level as the Great Depression? Not necessarily. Here is what the story really is:

The American dream of homeownership has felt its biggest drop since the Great Depression, according to new 2010 census figures released Thursday.

The analysis by the Census Bureau found the homeownership rate fell to 65.1 percent last year. While that level remains the second highest decennial rate, analysts say the U.S. may never return to its mid-decade housing boom peak in which nearly 70 percent of occupied households were owned by their residents…

Nationwide, the homeownership rate fell to 65.1 percent – or 76 million occupied housing units that were owned by their residents – from 66.2 percent in 2000. That drop-off of 1.1 percentage points is the largest since 1940, when homeownership plummeted 4.2 percentage points during the Great Depression to a low of 43.6 percent.

So the percentage drop is what is important here: it fell from nearly 70 percent in the mid-2000s to 65.1 percent today. This is similar to the 4.2% drop during the Great Depression. But notice: the homeownership rate in 1940 was 43.6 percent while it is still above 65% today. Overall, we are ahead of the 1940 figures even though the homeownership drop suggests that this recent period has had a similar effect on homeownership as the Great Depression.

Another interesting piece of news from this Census data on homeownership:

Measured by race, the homeownership gap between whites and blacks is now at its widest since 1960, wiping out more than 40 years of gains.

This is not good. The homeownership rate for blacks and Latinos increased small amounts from 2000 to 2010 but the gap has widened. Perhaps the American Dream, at least the homeownership part, has never truly really been available to everyone.

A call for better macroeconomic statistics

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As the economic crisis continues, one blogger suggests American macroeconomic statistics are “pretty weak” today:

In particular, the data coming out of the Bureau of Economic Analysis at the beginning of 2009 was way off. Here’s Cardiff Garcia, introducing an interview with Fed economist Jeremy Nalewaik:

The initial GDP estimate for the fourth quarter of 2008 showed that the economy contracted by 3.8 per cent. It was released on January 30, 2009 — about three weeks before Obama’s first stimulus bill passed. That number was continually adjust down in later revisions, and in July of this year the BEA revised it all the way down to a contraction of 8.9 per cent.

The BEA is happy to try to explain what happened here — but whatever the explanation, the original 3.8% figure was a massive and extremely expensive fail. It was bad enough to be able to get a $700 billion stimulus plan through Congress, but if Congress and the Obama Administration had known the gruesome truth — that the economy was contracting at a rate of well over $1 trillion per year — then more could and would have been done, both at the time and over subsequent months and years. Larry Summers warned at the time that the risks of doing too little were much greater than the risks of doing too much; only now do we know just how right he was on that front. (And even he didn’t push for a stimulus of more than $700 billion.)…

When I told Cardiff that the status of macroeconomic data-gathering has been declining for decades, I was making two separate statements — first that the quality of statistics has been declining, and secondly that the status of economists collating such statistics has been declining as well. Once upon a time, extremely well-regarded statisticians put lots of effort into building a system which could measure the economy in real time. Today, I can tell you exactly how many hot young economists dream of working for the BEA on tweaks to the GDP-measurement apparatus: zero.

Sounds like there is work to do. This commentator seems to suggest the government needs to offer the kind of money that would attract economists to this task. Are there economists out there right now who could handle this job and all it takes it some more money?

If we were looking at the causes of economic crises or perhaps what sustains them, could statistics really play a large role? Even with the best statistics, policymakers can still make bad decisions. But I suppose if the foundation of policy, the statistics that we trust to tell us what is really going on or what might, is faulty, then perhaps there is really little hope.

At the same time, I would suggest this isn’t only a macroeconomic problem: the world is complex, we want to tackle difficult problems, we are very reliant on statistical models, and there is more and more data to work with and collect. We need a lot of good people to tackle all of this.

Comprehending the office and retail space in an edge city

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After explaining the concept of an edge city to my American Suburbanization class, a discussion arose about how much space these places really have. When defining the edge city, Joel Garreau had these as two criteria (out of five total): “has five million square feet or more of leasable office space” and “has 600,000 square feet or more of leasable retail space.” This is a lot of space, as much as a smaller big city, but can still be hard to understand.

For example, there is much more commercial and retail space in the exemplar of the edge city: Tysons Corner, Virginia.

Around 2007 Tysons Corner had 25,599,065 square feet (2,378,231.0 m2) of office space, 1,072,874 square feet (99,673.3 m2) of industrial/flex space, 4,054,096 square feet (376,637.8 m2) of retail space, and 2,551,579 square feet (237,049.4 m2) of hotel space. Therefore Tysons Corner has a grand total of 33,278,014 square feet (3,091,628.7 m2) of commercial space.

How do we put this in more manageable terms?

1. Garreau compares this suburban space to the office and retail space in existing cities. The 5 million square feet of office space “is more than downtown Memphis.” While we may have traditionally associated this much office and retail space only with the downtowns of big cities, now concentrations of this space can be found right in the middle of the suburbs. This is unusual because suburbs are often portrayed as bedroom suburbs, places like people live and sleep but have to work elsewhere.

2. Compare this space to large buildings. The Willis (Sears) Tower in Chicago has 4.56 million square feet of space, 3.81 million rentable. So an edge city would have at least slightly more space this notable office building though perhaps it is difficult to visualize this space since it is a skyscraper and each floor seems smaller. An ever bigger building, The Pentagon, has 6.5 million square feet, more than the lower threshold for an edge city. Therefore, Tysons Corner has nearly 4 Pentagons of office space. Comparing this edge city space to shopping malls, Woodfield Mall in Schaumburg, Illinois (an edge city itself) has 2.7 million square feet while the Mall of America has a total of 4.2 million square feet.

3. We could measure edge cities in terms of square miles or acres and then compare to bigger cities. Square miles make some sense: Tysons Corner is 4.9 square miles while Memphis, a city Garreau says has downtown space similar to that of an edge city, is 302.3 square miles (on land). Acres are a little harder to interpret: a common suburban house lot is an eighth of an acre, a square mile has 640 acres (hence the dividing of the American frontier into 160 and 640 acre plots), and an acre has roughly 43,500 square feet. Then, an edge city with 5 million square feet of office space has about 115 acres of office space. Perhaps acres are best left to farmers.

In the end, I think Garreau made the right comparison to demonstrate the office and retail space within an edge city: we have some ideas about the size of downtowns of smaller big cities and the image of this amount of space existing in the suburbs is jarring.

The real America can be found at Wal-Mart

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I vividly remember what one professor told us one day in a sociology of religion class in graduate school: “If you want to find real Americans, just go to Walmart.” Several members of the class gasped – could the real America really be at Walmart, that exemplar of crass consumerism, low wages, and the loss of community life in America? This story from NPR makes a similar point:

The Wall Street Journal spotted the phenomenon recently. The headline: “Today’s Special at Wal-Mart: Something Weird.” “Almost any imaginable aspect of American life can and does take place inside Wal-Mart stores, from births to marriages to deaths,” observed the Journal‘s Miguel Bustillo. “Former Alaska Gov. Sarah Palin once officiated a wedding at the Wal-Mart in her hometown of Wasilla.”…

What is it about Walmart? As a species, we are fascinated by the place. The Web is awash with sites that scrutinize the Arkansas-based retailer’s every move. Walmart Watch, funded by the United Food and Commercial Workers Union, says its mission is to challenge the multibillion-dollar retail chain “to more fully embrace its corporate responsibilities.” The now-infamous and snarky People of Walmart posts photos of shoppers. Hel-Mart offers anti-Walmart merchandise, such as T-shirts that say, “Resistance Is Futile.” Videos of people praising, mocking, pranking, walking around, dancing in Walmart are continuously posted on YouTube…

Officially, Walmart explains the apparent zaniness this way: “Over the years, Walmart has become a microcosm of American life,” says company spokesman Lorenzo Lopez. “With stores serving millions of customers in communities nationwide, it’s not uncommon for us to see our share of what happens every day in cities and towns all across the country.”…

* Of the 3,822 Walmart stores, 2,939 are Supercenters, which means they are open 24 hours a day. So in virtually every county, 500 people work at Walmart, and there is a Walmart open every hour of every day, and every one of those Walmarts is being visited by 37,000 people a week — that’s 220 people an hour, in every Walmart, in virtually every county in the whole country, every hour of the day.

So how come there are not more sociologists doing studies at or about Walmart? I suspect many do not like the place – even though some may even shop at Target and other big box stores. But just because sociologists might disagree with the practices of Walmart does not mean that it shouldn’t be the focus of much research.

This story also illustrates something Joel Best likes to talk about: the scale of numbers. Some of the statistics about Walmart from the article include half of American adults visit Walmart each week covering 70 million hours and the company has 1.5 million employees. This is hard to visualize because these are big numbers. We know what a couple of hundred people looks like but to understand 1.5 million, we might need to make some comparisons such as this is about the population of the City of Philadelphia or is around the same size as the metro area of Nashville or Milwaukee. Another way to understand these big numbers is to break it down into how often something happens per hour or minute or second. In this article, this translates to “that’s 220 people an hour, in every Walmart, in virtually every county in the whole country, every hour of the day.” We know what roughly 220 people looks like so we can then grasp a little better the enormity of the figures.