Raw numbers vs. statistics

Following the arrest of Aaron Hernandez, who played tight end for the New England Patriots, a Facebook posted the CNN screen cap above. If you ask a member of the general public how the arrest rate in the NFL compares to that of other sports, or even the country as a whole, they might guess that it is higher, not lower. This is a good example of the difference between raw numbers and statistics and is an important part of the information literacy that students should learn in research methods and statistics courses. Exploring the numbers in a bit more depth (and ignoring the fact that the type of crime, which could easily influence perceptions, is not noted), we can see where misconceptions in the general public might come from.

Major League Baseball has 30 teams and each team has 25 players on its active roster, with up to 40 players signed at any given time. Assuming that these statistics are per year (another good question to ask!), if 2.1% of MLB players are arrested that means that 15.75 (for a 25-player roster) or 25.2 (for a 40-player roster) players would be arrested each year out of 750 or 1200 total players, respectively.

The National Basketball Association has 30 teams and each team has 15 players. If 5.1% of NBA players are arrested in a given year, that results in 22.95 players arrested out of 450 players. As you can see in the table above, this is above the national average. David Stern, the NBA’s commissioner, has famously tried to clean up the league’s image by enforcing a dress code since the beginning of the 2005-06 season.

The National Football League has 32 teams and each team has 53 players, more than twice the active roster of MLB teams and more than three times the number of players on an NBA team. If 2% of NFL players are arrested in a given year, this means that 33.92 players will be arrested out of 1696 total players. A more in-depth exploration of the rate of arrest for NFL players compared to the general population is available here.

If each arrest leads to a news story, it is easy to see how the general public could think that NFL players are getting arrested at a higher rate than their counterparts in other professional sports. Looking at statistics, however, reveals the truth that the large rosters of NFL teams that lead to more media coverage of arrests. A discussion of an easily-accessible topic like this might lead into a more detailed exploration of the selective coverage of certain types of crime by the media, leading to public perceptions about the rate of crime among various race and social class groups.

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A reminder about quantitative data for first-year grad students in love with the GSS

They can be just as “fuzzy” as qualitative data.

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Researching 5-hour Energy

If you have watched TV in the past few months you have probably seen the above commercial for 5-hour Energy that would provide a good introduction to misleading media deceptions in a research methods or statistics course. The commercial touts the fact that they surveyed over 3,000 doctors and what they found was amazing. What was apparently so amazing was the fact that 73% of doctors surveyed said that they would recommend 5-hour Energy. Wait, no, that’s not it. 73% of doctors surveyed said that they would “recommend a low-calorie energy supplement to their healthy patients who use energy supplements.” That’s not quite the same thing, is it?

Unlike those “look how great we are” commercials that say things like “four out of five dentists recommend Trident,” the claims made by 5-hour Energy seem more along the lines of “we spent a lot of money to do this survey and we’re going to advertise the results no matter what they show!” In fact, the small print (visible if you enlarge the ad above) is incredibly honest (for a commercial, at least) about the actual methods and findings. Here is the small print in order:

• All doctors surveyed identified themselves as primary care physicians
• Two surveys were conducted to determine the opinions of primary care physicians regarding energy supplements and 5-hour Energy: 1) an online survey of 503 participants; and 2) an in-person survey by 5-hour Energy representatives of 2,500 participants (50% of those approached). In both, participants agreed to review materials regarding 5-hour Energy consisting of label and basic description of its ingredients. Of the 503 online and 2,500 in-person, over 73% said they would recommend a low calorie energy supplement to their healthy patients who use energy supplements.
• Of the 73% of primary care physicians who would recommend a low calorie energy supplement to their healthy patients who use energy supplements, 56% would specifically recommend 5-hour Energy for their healthy patients who use energy supplements.
• Of all primary care physicians surveyed, 47% would specifically recommend 5-hour Energy for their healthy patients who use energy supplements.

So, 5-hour Energy has spent a lot of money on a survey and advertisements to tell people that 27% of doctors would not recommend low-calorie energy supplements to their healthy patients, even if they already use energy supplements. Furthermore, only 47% of the doctors surveyed would actually recommend 5-hour Energy. This is a far cry from the “four out of five dentists” claims. These results are amazing, all right. Amazingly unimpressive!

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99% of you agree with this post

The following video is useful for a class discussion about the difference between scientific and non-scientific polls.  99% of you agree that it is also useful for your enjoyment.

Vodpod videos no longer available.

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