Related posts:

1. Famous people commissioning surveys: The Dilbert Guy

A recent series of events at Fox News involved not only a mistake in reporting survey data, but a subsequent refusal to acknowledge the mistake, even after it was pointed out.  The timeline of events is as follows:

1. On November 23, 2009, after a "series of [on-screen] mistakes," Fox News implemented a zero-tolerance policy for on-screen errors.
2. On December 1-2, 2009, Rasmussen Reports, a well-known public opinion polling firm, conducted a national survey to determine the views of Americans on the issue of global climate change.  Survey question #3 asked, "In order to support their own theories and beliefs about global warming, how likely is it that some scientists have falsified research data?" Rasmussen reported the responses to this question as follows:
   

   35% Very likely
   24% Somewhat likely
   21% Not very likely
   5% Not at all likely
   15% Not sure

3. On December 3, 2009, Rasmussen Reports published a summary of the results of the survey in which they noted, among other things, that:
   

   "Fifty-nine percent (59%) of Americans say it’s at least somewhat likely that some scientists have falsified research data to support their own theories and beliefs about global warming. Thirty-five percent (35%) say it’s Very Likely. Just 26% say it’s not very or not at all likely that some scientists falsified data."

   (This was in fact an accurate summary of the survey data from survey question #3.)

4. On December 4, 2009, Fox News broadcast a 1-minute segment in which a graphic (created by Fox News) was displayed which incorrectly summarized the data from survey question #3, and three commentators briefly discussed and interpreted these (incorrect) data.
5. On December 8, Media Matters for America, a non-profit media watchdog group, sent an open letter to Fox News pointing out the error in the Fox News graphic, and suggested that this might be a case that merited a reprimand under Fox's new zero-tolerance policy.  Fox News responded that there was no error in the graphic, and thus no need for any reprimand.

If you look at the graphic, it seems pretty clear what happened: whoever created the graphic only read the Rasmussen summary of the survey data, and not the breakdown of the actual percentages for this question.  This person no doubt assumed the three percentages quoted in the summary paragraph represented all of the answer choices for the survey question, when in fact the 59% number combined the responses for Very Likely and Somewhat Likely into a larger category of "at least somewhat likely."  (This combining of response categories is done all the time when reporting on survey data.)  The Fox News graphic implies that the Very Likely group is separate from the 59% "combined" category, when in fact it's a subset of it.  As pointed out by a number of observers, reporting the percentages as Fox did clearly distorts the survey data, even making it appear that the total number of survey responses exceeded 100%.

While many people may disagree about the degree to which Fox News or Rasmussen Reports display a conservative bias, or the degree to which Media matters displays a liberal bias, or the appropriateness of some sort of reprimand under the Fox News zero tolerance policy, the one thing that is undeniable is that Fox News made a mistake when creating the graphic.  Yet, when the error was pointed out, Fox News simply claimed that while "the presentation wasn't perfect," there was no error in the graphic.

While this wasn't perhaps the worst mistake ever made, it was a mistake, and while there's no shame in making a mistake, there is shame in attempting to cover it up.  For a major news organization to refuse to acknowledge such a clear error in reporting simple facts is unconscionable.

Related posts:

1. Famous people commissioning surveys: Trent Reznor
2. Famous people commissioning surveys: The Dilbert Guy

Just wanted to send a quick shout out for The Drunkard's Walk, a really neat book on "how randomness rules our lives," written by Leonard Mlodinow, a physicist at Caltech and a collaborator with Stephen Hawking on the book A Briefer History of Time.

When I write a review of a math-related book, I generally assume that it will be largely ignored by anyone's who's not a math geek.  While that may often be true, in this case I happen to know for a fact that this book has appeal beyond the math geek crowd because after I mentioned Mlodinow's description (in Chapter 3) of the controversy that surrounded a fairly well-known math problem (the Monty Hall Problem), my wife was so fascinated that not only did she read the chapter for herself, she actually wrote a blog post about it.

In much the same way that Levitt and Dubner's book Freakonomics drew us into the use of economics by applying it to fascinating real-world examples, Mlodinow draws us into understanding the role of probability and randomness in our lives by exposing the flaws in the way we typically think about a number of common situations such as the skill of successful stockbrokers, the quality of wine and vodka, and what makes a really good actor.  Often, where we think we see clear patterns or signs of cause and effect, what we really see is just the role of chance.

Mlodinow really does an excellent job at making a confusing subject a little less confusing, and he also makes us feel a little better about how confused we all are by reminding us of Martin Gardner's comment that "in no other branch of mathematics is it so easy for experts to blunder as in probability theory."

Related posts:

1. Video book review: Icarus At The Edge of Time
2. Sometimes you just need a little help

The online marketing and web analytics company Hubspot recently reviewed some data that they collected from some of their customers, and the data provide some pretty interesting numbers for people who wonder if blogging is really all that useful as a business marketing tool. Hubspot looked at website traffic and other stats for approximately 1500 of their US and Canadian customers, most of whom were small- and medium-sized businesses. Roughly half of these businesses had a blog as part of their website, and the other half did not.

The results were pretty impressive.  Overall, compared to the companies that did not have a blog, the companies that were blogging had:

• 55% more visitors to their website
• 97% more inbound links
• 434% more indexed pages

While there are many details we don't have about their sample and their data collection approach, and while it's important to note that correlation does not imply causation, these are still some interesting numbers to consider.  In fact, the comments section of the blog post provides a great place to start.

The author of the post notes that for the purposes of this study, the operational definition of a "business that had a blog" was simply one that a) had blogging software installed on their website, and b) had more than one blog post.  This is a pretty low standard; it makes one wonder if businesses that blog more actively tend to see even better results.

Several of the commenters noted that the results reported by Hubspot matched results they had seen with their own blogs, and one of the commenters said he works for a company that also helps businesses "get the most out of a blogging program" and that they "track similar metrics and have similar findings."

A number of commenters pointed out that there were many things unknown about the businesses in the sample, and that some of those things might have a big effect on how one interprets the data.  For example:

• Perhaps the blogging businesses are simply more "digitally savvy" in general, and would be connecting more effectively with potential customers even without a blog.  In particular, perhaps the blogging businesses conduct more effective SEO or PPC campaigns, send out more email, twitter, or facebook alerts, and/or simply have more or better content on their site.
• Perhaps the blogging businesses already have a better online reputation than the non-blogging businesses.
• Perhaps the blogging businesses are simply larger and thus have more resources to devote to the quality of their website.

One commenter noted that focusing on blogging and increased site visits may actually be a distraction, suggesting:

Companies that [already] have a lot of site visitors tend to start blogging.

Blogs tend to increase fluff visits and have little effect on the bottom line, other than draining marketing resources into writing blog entries.

Blogs that are about blogging tend to attract a lot of commenters whose main purpose is really to get another link to their own blog out there.

The blog community perpetuates itself. The average consumer is relatively untouched.

Still, even with the limitations noted above, this is in fact a good "starter set" of data.  As long as you don't take these data to mean that all you have to do is start a blog on your website and your business revenue will magically increase, you might find that they provide you with some insights that could help inform the marketing plans for your own business.

Related posts:

1. Businesses Unhappy With Google for Making Their Customers Happy
2. A Simple Online Data Collection System: SurveyMonkey vs. A Custom Solution
3. Famous people commissioning surveys: The Dilbert Guy

My first son is currently 14 and a half, and while he's not driving yet he has a few older friends who are.  Until recently, one of our house rules was: no riding in a car with a teen driver.  Though it was inconvenient at times (like when I had to drop off The First at some event to which "everyone else" got to ride with one of his friends), I was pretty pleased with this rule; it was simple, easy to enforce, and provided my son with a reasonable amount of protection from the dangers of teen drivers.

A couple of months ago, however, one of The First's best friends got his driver's license, and suddenly he was ready to re-negotiate the rule.  After discussing the matter with my wife, I reluctantly agreed that forbidding him to EVER ride in a car with a teenager might be unnecessarily strict, so the issue became one of "under what circumstances would it be allowed."

I did a little research and found not only some useful stats to inform our eventual agreement, but also a pretty nifty online tool from Allstate called a Parent-Teen Driving Contract, which we modified slightly to create our own Teen Rider Agreement.  I found the process of creating the document to be very valuable, as it forced me to consider what restrictions I felt were most important and why.  The process also provided opportunities for some good discussions with The First about safe driving.

The one rule in our Agreement that The First objected to most strenuously was the one about not riding with "any teen driver who has had their license less than 6 months," since this ruled out riding with his newly-licensed friend this summer.  The wife and I insisted on this one, however, and even discovered later that his friend's parents had implemented very similar rules at their house.  It turned out that even if we would have allowed The First to ride with their son, they wouldn't have.  I thought that was pretty cool.

During my research, the stats I found most interesting (in addition to those that showed just how dangerous teen drivers are in general) had to do with the increased risk of accidents when teen drivers were a) driving at night, and b) carrying other teen passengers.  Here are links to some teen driving statistics that I found most useful:

• Fatality Facts 2007, from the Insurance Institute for Highway Safety.  There's a neat graph about 2/3 of the way down the page.
• Reader's Digest's Anatomy of a Teen Car Accident.  The slideshow is kind of annoying, but the stats are very intriguing.
• The CDC's Teen Drivers Fact Sheet.
• Carrying Passengers as a Risk Factor for Crashes Fatal to 16- and 17-Year-Old Drivers.  This one's a pdf, the source for many of the stats you'll find online regarding the risks of teen passengers and driving at night.  Only 6 pages, and remarkably readable.

No related posts.

I go to a really nice gym.  They have not only a large weight room with a ton of nice equipment, but also two swimming pools, two full-size basketball courts, several racquetball courts, a rock-climbing wall, and two large rooms for aerobics classes and such.  They also have a full-service child-care center, a small cafe, and a place where you can get massages and facials.  (The only reason I get to go there is my wife works at a place that provides a family gym membership to all its employees.)

The locker rooms are really nice, too.  They have both dry-heat and steam saunas, plus they provide towels so you don't have to bring your own.  Recently, several of these signs were posted in the locker rooms:

"Holy cow," I thought, "17,000 towels a day, that's a lot of towels!"  I figured a lot of people must really be wasting towels and that it was a good thing that the gym owners posted those signs so those towel-wasters would wake up and stop wasting so many towels.  I was also feeling pretty pleased with myself, because I only use two towels every time I visit.

But then I got to wondering just how many towels, on average, people were actually using.  It would depend, of course, on how many people came thru the gym on an average day, but I didn't have that information.  I asked at the front desk if they could tell me, but was told that that information was proprietary and they weren't allowed to give it out.  (I guess they don't want potential competitors to know how many people are using their gym?)

So I started thinking about it.  If 1,000 people a day came thru the gym, that would be an average of 17 towels per person, which would be absolutely outrageous; nobody needs to use 17 towels when they go to the gym.  But if, say, 5,000 people a day were coming thru the gym, that would be an average of only 3.4 towels per person; maybe the people who were using 5 or six towels per visit could stand to cut back, but 3.4 towels per person didn't seem outrageous.  On the other hand, I couldn't imagine that 5,000 people a day were coming thru the gym; heck, 1,000 people a day sounded high to me.

Without knowing the actual number of people who came thru the gym, I couldn't figure out whether we were using too many towels, and the gym owners weren't telling.  So I did the next best thing: I counted them.

No, I didn't actually count every single person coming into the gym one day, but I did count every person coming into the gym for 30 minutes one afternoon, roughly between 3:30pm and 4pm.  During that time, 115 people, adults and children, walked thru the doors, which is approximately 230 people an hour.  The gym is open 24 hours a day, though I suspect there are a lot fewer people that come during the late night and early morning hours.  So I figured that between 6am and 9pm, 230 people an hour would come thru, and between 9pm and 6am only about a quarter of that, or 58 people an hour, would come thru.  Thus:

230 ppl/hr x 15 hrs = 3450 people

58 ppl/hr x 9 hrs = 522 people

3450 + 522 = 3972 people per day

17,000/3972 = 4.3 towels per person

One could interpret these numbers different ways.  Since I only use two towels per visit, 4.3 seems a little high as an average, but I typically only go to workout in the weight room and use the steam room and then take a shower.  If someone's going to spend several hours at the pool, plus maybe play some basketball then take a shower, maybe using five or six towels isn't so outrageous.

There are other things to take into consideration as well.  It's not clear from the posted sign whether the 17,000 number refers to full-size towels only, or includes the small hand towels which many people use to wipe sweat from their faces and hands during their workout.  If the 17,000 includes hand towels, the 4.3 average towel number starts to sound even more reasonable.  And of course, my numbers are only an estimate based on a single 30 minute sample on a single weekday afternoon; the number of people coming to use the gym no doubt varies from weekdays to weekends, from one week to another, from one month to another, etc.

The larger point, however, is that being told that this facility provides 17,000 towels per day doesn't give us enough useful information to determine whether we're using too many towels or not.  I suspect that it costs a good bit of money to wash and dry all those towels every day, and the owners were hoping to get us to cut back on our towels usage by posting a number that sounds really big, thus generating the kind of "Wow, that's a lot of towels" reaction that I initially had.

It would be even better, however, to actually know how many towels we're using on average.  Then we might be able to decide whether we're really using too many.

Update: Reader Jennifer was somehow able to get the gym staff to give her the information that they made me work for.  (Maybe she said please?)  The official word is that the average person at my gym is using 5 full size towels per visit, and yes, I agree that seems a little high.

For those keeping score at home, if the average person is using 5 towels per visit, and a total of 17,000 towels per day are being used, that means approximately 3,400 people are coming thru the gym every day.

No related posts.

The current national and international concern over the swine flu (aka influenza A, H1N1) outbreaks has created a fair amount of concern among many.  With so many media outlets anxiously reporting on the latest suspected or confirmed cases, or on different people's or institutions' reactions to the disease, a little perspective could be helpful.

A recent story on NPR's Morning Edition reported on the number of young children who are injured or killed each year due to falling furniture, specifically falling TVs.  Researchers at Nationwide Children's Hospital in Columbus, Ohio, analyzed data from the federal Electronic Injury Surveillance System.

...They looked at all emergency room patients under 17 years old who suffered furniture or TV tip-over related injuries from 1990 to 2007.

They estimate a total of 264,200 children and adolescents were treated for such injuries during the 18-year study period. This averages to 14,700 injuries among children every year. Three-hundred died as a result of their injuries during this period.

Thus we have approximately 14,700 US children injured each year, and approximately 17 US children who die each year, as a result of a TV or other piece of heavy furniture falling on them.  As of today (May 4, 2009), there are 253 confirmed cases of swine flu in the US, another 98 suspected cases, and one death.  (Note that the swine flu numbers are counting people of all ages, not just those under 17.)

This is not an attempt to say that swine flu, or any other type of influenza, may not be a dangerous illness, especially for young children. Approximately 36,000 deaths (children and adults) are associated with influenza each year in the US, roughly the same number of Americans who are killed in automobile accidents each year.  There have also been three "notable" worldwide flu pandemics since 1900, and the World Health Organization "warns that there is a substantial risk of an influenza pandemic within the next few years."

But it is also good to keep in mind that the biggest threats to our physical safety are usually not something as dramatic as the latest worldwide infectious disease outbreak, but something as mundane as heart disease, an automobile accident, or falling furniture. We live in a world that can be dangerous, but it's good to keep those dangers in perspective.

Update: Wired magazine had a neat article in their July 2009 issue in which they compared the H1N1 virus (fatality rate 0.7 percent) with the 1918 flu pandemic (fatality rate 5 percent) and the fictional virus from Stephen King's novel The Stand (fatality rate >99 percent).  Just the graph (below) is priceless, but you should also click over to read the short article.  Very nicely done.

Related posts:

1. Statistics in iPhone article unnecessarily confusing

A recent post at wral.com, a local news site here in Wake County, NC, is titled, "Wake County could eliminate 100 positions," a headline which is unfortunately all too common in this time of rising unemployment.  The post goes on to tell us a number of other things, including that the elimination of these positions still has to be approved by the Wake County Board of Commissioners, that the cuts could save $3 million at a time when the county is facing a $20 million budget shortfall due to lower-than-projected tax revenue, and that the commissioners have said that "raising taxes is not an option."

All of this is useful information, yet the article doesn't tell us one thing that would help us make more sense out of this "100 positions" number: how many people are employed by Wake County?  If Wake County employs, say, 10,000 people, cutting 100 positions means only 1% of their employees will lose their jobs.  On the other hand, if Wake County employs 500 people, cutting 100 positions means 20% of their employees will lose their jobs.  We need to know how many people work for Wake County in order to know if "100 positions" is a big number or not.

A little bit of googling led me to the wakegov.com website, where I found a pdf of Wake County's Fiscal Year 2009 Recommended Budget.  The third paragraph on page 15 of the pdf tells me that "Wake County has over 3700 employees."  (Note that this does not include the approximately 18,000 people employed by the Wake County Public School System.)  With this information, I can see that Wake County is considering the elimination of a little less than 3% of their workforce.

If the intent is to convey meaningful information, it's not enough to report a number and consider the job finished; one must also provide enough context to make sense of the numbers being reported.  In this case, merely reporting that Wake County plans to cut 100 positions, without also reporting the total number of Wake County employees, is not helpful.  One might just as well say, "Wake County plans to cut some positions."

Related posts:

1. Statistics in iPhone article unnecessarily confusing
2. 17,000 towels? That must be a lot, right?
3. Questionable numbers: US Chamber of Commerce

Journalist Michael Kinsley recently wrote an article for Time magazine in which he criticizes the Social Security system for providing "entitlement" income for those who don't really need it.  The starting point for his critique is a number he got from a Federal Reserve report that says the average net worth of American families whose head of household is between 65 and 74 years of age, is $690,900 (in 2004 dollars).  Kinsley argues that with this kind of net worth, the typical American family is not in nearly the dire financial straits that are often depicted by the media.

On the face of it, this looks like a reasonable argument.  The problem with it is that the number that he's using to describe the "average" net worth (the arithmetic mean) is a lousy measure to use when describing net worth.  A much better measure, and the one used almost universally by those who want to describe things like the average income or net worth of a large group of people, is the median.

A typical way to explain the difference in these two measures is to think of five people in a bar.  Let's say the net worth of each of the five people in the bar is $100K, $150K, $175K, $200K, and $225K.  The mean net worth of the people in the bar is $170K (add the five numbers and divide by five), and the median is $175K (the "middle" number if we line the five numbers up from smallest to largest).  Since the five values are relatively close together, the value of the mean and the value of the median are also relatively close.

If Bill Gates walks into the bar, however, with his net worth of roughly $58 billion, the mean net worth of the bar patrons suddenly becomes roughly $9.7 billion, while the median becomes $187.5K (the midpoint between the two middle values $175K and $200K).  This is why the median is a much better way to describe the average net worth of a group of people: a single outlier can make it look like the people in the group are a lot wealthier than they really are.

In the case of the Time magazine article, Kinsley could have easily used the median net worth number, because it was in the same table where he found the mean value (page A8 in the Federal Reserve report, for those following along at home).  The median value is $190,100 and maybe this explains why Kinsley didn't use this number, even though it's a more accurate way to describe the average net worth of a large group of people: it doesn't really support his argument that the "average" American family doesn't need the Social Security safety net.

(Thanks to Dean Baker for turning me on to the Kinsley article.)

Related posts:

1. Questionable numbers: US Chamber of Commerce
2. 17,000 towels? That must be a lot, right?

Below is a nifty graph which I first saw displayed in a post by Clay Shirky at boingboing.

The graph shows the annual return on the S&P stock index for every year going back to 1825.  The heavy black line in the middle represents a zero return; if a year is listed to the right of the black line then the S&P index yielded a positive return for that year, and if it's listed to the left, then it had a negative return for that year.  The little boxes that contain the years are stacked in groups of 10%.  For example, the year 2006 (at the top of the second highest stack) had a total annual return somewhere between 10% and 20%, while the year 2000 (at the top of the third highest stack) had a return somewhere between 0% and -10%.  And yes, 2008 is all the way over to the left.

This type of graph is called a histogram, and is a fairly common way of displaying these kind of data, which are called "frequencies."  The horizontal axis of the graph represents a range of intervals (in this case, stock returns expressed in percents), and the vertical axis merely shows the number of years which fell into each range.  One of the things I like about histograms is that they can translate a bunch of confusing numbers into a picture which makes a very clear point.  In this case, just a quick look at the histogram makes it clear that for the past 183 years, the number of years in which the S&P index had a positive return is greater than the number of years in which the index had a negative return.  (Here's another histogram that makes this point in a slightly different way.)

[The graph shown above is actually a slightly more readable version of a graph originally prepared by a group called "Value Square Asset Management" of Yale University though I couldn't figure out exactly who this group is, and it seems I wasn't the only one.]

Looking into this graph a little more, I discovered that the returns for each year are not calculated based on the same data.  For the years from 1957 to 2008, the returns are those calculated for the S&P 500.  Prior to 1957 the S&P 500 did not exist, but from 1923 to 1957, Standard and Poor's did have another index called the S&P 90, which was based on 90 stocks rather than 500.  The returns for the years 1825 to 1923 (almost 100 years of the 183 years in the graph) apparently come from a paper published in 2000 which you can download for free here.  (You can also pay $31.50 for the same paper here, which I don't entirely understand.)

All of which says something else about the value of graphs.  While the whole point of most graphs is to visually summarize (and simplify) a bunch of data so as to present them in an understandable format, it's important to remember that any time you simplify something complicated (like stock market returns for 183 years), you're probably going to lose a lot of the details.  While trading off some complexity for clarity may in fact be a good trade, it's still a good idea to remember that not every detail about a set of data is going to show up in a graph.  I don't know enough about economics to know whether the differences in stock returns calculated for the three different time periods discussed above substantially compromises the value of this graph, but if you look at the graph and never ask where the data come from, you don't have the opportunity to consider it.

Related posts:

1. Hubspot data suggest blogging is good for business
2. A Simple Online Data Collection System: SurveyMonkey vs. A Custom Solution