While sitting in the car waiting to give my sister a ride back from a volleyball game, I came up with a new road trip game. There was nothing interesting on the radio stations I usually listen to, so I switched to AM and started scanning. Unsurprisingly, there wasn’t anything interesting on. I heard a few questionable bible lessons, some ballgames, the usual political shows, a french broadcast I could almost understand, bad music, and lots of advertisements. I decided to listen to one of the political shows for a while. After a few minutes I got tired of the false ‘facts’ and incoherent reasoning, and switched to another talk station. It didn’t take long to hear misleading statistics, so I tried again. I made it around the dial three times before the team made it out of the locker room.

This gave me the idea for a new car game: AM Statistics or Check your arithmetic.

The rules

1. Pick an AM talk radio station
2. Listen until you hear an obvious mathematical or statistical error
3. Tune to the next talk radio station
4. Repeat

If you are good, you won’t have to stay on any one station for long. Try to be the first one to spot an error; or to play alone, see which program requires the fastest station switching.

Example errors

• You’ll constantly notice missing numbers, typically involving citing a partial statistic to support a conclusion, but if an extra sentence of clarification and detail was added, the conclusion would have to change.
• You’ll hear the mistake of semiattachment. This means using numbers that appear to be related and good measures, but aren’t. Knowing or noticing the proper definitions helps in finding this error, but it’s often obvious even from the detail included.

If you have read How to Lie With Statistics, you’ll have a hard time not finding these errors. These are usually pretty easy to spot even without much subject familiarity. If you know the subject or statistics, there will be plenty more.

Expanded rules

To make the game go even faster, you can expand the rule from errors in math and stats by including logical errors. You’ll probably have to keep your hand on the dial if you are playing Find the Fallacy.

Example errors

• It isn’t hard to find self contradictory statements. If you make it past a commercial break, you’ll likely hear the argument of the previous segment used on a different topic to reach the opposite conclusion as in the last segment.
• If you are paying attention, equivocation will constantly jump out at you. This is when a term is used to mean different things in the same argument. You’ll often hear equivocation used in a single sentence.
• Even if you aren’t good at finding the other errors, it’s hard to miss the constant ad hominin attacks.

It shouldn’t take too long to make it around the dial. You could even expand the rules to include any factual errors. If you have passed a history or science class, this will likely be too easy. This game works even better if you have the misfortune of watching cable news.

Paul Krugman provides a good example of using misleading statistics in his latest column.

GMAC Insurance released their 2010 National Drivers Test results. The findings are interesting:

• If taken today, 18.4 percent of drivers on the road – amounting to roughly 38 million licensed Americans – would not pass a written drivers test exam.
• The national average score was 76.2 percent; a score below 70 percent is considered failing.
• Average test scores in 2010 continue to show a slight trending downward, from 76.6 percent in 2009 to 76.2 percent this year and a drop of almost 2 percent from the national average in 2008 (78.1 percent).
• With Age Comes Wisdom: The older the driver, the higher the test score. Males over 45 earned the highest average score.
• Factoring in margin for error, the average test score was significantly higher among males than females (78.1 percent male versus 74.4 percent female). Females also had a higher failure rate than males (24 percent female versus 18.1 percent male).

I’m not particularly surprised at the results. It can be hard to remember which of several similar answers is correct, which partially accounts for the low score; but this isn’t an excuse on something this important. The way I see it, the results are evidence that nearly one fifth of the licensed drivers in the country should have their licenses suspended until they re-pass their licensing requirements. Even this is optimistic. A survey like this can’t distinguish between book knowledge and its application. How many people can pass the test but never follow the rules afterward? This could be examined by including both the scores on the driver’s written tests and state accident data in the analysis.

Even in the wildly optimistic case that all drivers are able to re-pass the driver’s licensing tests after driving for a few years, it still wouldn’t be enough to ensure safe roads. The driver’s tests are currently only for the absolute minimum required knowledge and skill to drive a car on public roads, safe driving requires much more skill and awareness. A good step toward this level of driving is to take the ABATE or MSF motorcycle safety test. I think that passing one of these courses should be a prerequisite to applying for a car learner’s permit. This would make the roads much safer.

The GMAC test is online so you can try it yourself. Then you should read my page on safe driving around bicycles.

Source: 2010 GMAC Insurance National Drivers Test via AOL Autos via USA Today. Note that this was an online survey.

I never would have guessed, but apparently drivers in Fort Wayne are involved in accidents 16.3% less than the average driver in the 200 most populous cities in the USA. Just think how much safer we could be if Indiana had slightly less easy licensing tests.

Study found through ‘For safe driving, city ranks No. 11’ in the Journal Gazette.

This is much higher than I expected, so I decided to check the numbers myself. I found the data on the CDC website and plotted it along with moving averages to define ‘generation’:

Huh. That’s much higher than I expected. I’d figured it would be around a tenth that rate, and at most up to half that rate. These higher than expected numbers mean that one-quarter is a reasonable estimate. Depending on how ‘my generation’ is defined, the one-quarter figure may be a little high, but it is at minimum one-fifth. Under any reasonable definition, there is no way I’d consider 1/5 to be ‘rare.’ It’s a stretch to call one-tenth rare. I’d hesitate to call 1/36—the probability of rolling snake eyes—rare. I’d consider a general definition of rare to start around 1/500, approximately the probability of drawing a flush in poker. For diseases, the NIH uses a definition somewhere around 1/1500. Even if the abortion rate in the USA is lowered to one sixth the current level, it still wouldn’t fit in the loosest of these definitions of rare. This means that, even for a generous definition, we have a long way to go before abortion could be considered ‘rare.’ It’s worth noting that the pro-abortion politicians mostly stopped using the ‘rare’ statement a couple years ago, showing that they were probably never serious about it.

Note: Data are from the US Centers for Disease Control and Prevention. The CDC MMWR abortion reports are released at the end of November with a three year lag. ‘Fetal loss’ other than induced abortion is excluded from the data I used in the plots. The numbers include both surgical and medical (non-surgical) abortions. Data is abortion rate per 1000 live births, I converted it to a fraction to clarify the plots. The full report is worth a look. Since it is split between two tables in the report, here is a plot of when during a pregnancy abortions are performed:

Sources:

• CDC Morbidity and Mortality Weekly Report, Surveillance Summaries, Abortion Surveillance — United States, 2006, November 28, 2008 / Vol. 57 / No. SS-13
• CDC Morbidity and Mortality Weekly Report, Surveillance Summaries, Abortion Surveillance — United States, 2006, November 27, 2009 / Vol. 58 / No. SS-8
• The 2004 Democratic National Platform for America. Includes ‘Abortion should be safe, legal, and rare.’
• The 2004 Democratic National Platform. Uses ‘safe and legal abortion, regardless of ability to pay.’

This doesn’t match the distribution I expected. After looking at the House, I examined the results for the Senate:

This looks a little broader than the House, but still not quite as biased toward long times in office as I had expected. To be a little more thorough, I calculated basic summary statistics:

It turns out that careerism isn’t nearly as bad as I thought. Of course, the summary stats don’t quite give the true answer, because they don’t take into account that this is the time served so far by those currently sitting in congress. What I really want to see is the total time served by all those now in congress, after they have retired or lost an election. Basically, I’d expect this to show a result slightly lower than the true average.

A little reading shows that the average reelection rate is about 84% (for 1982 to 1994, I don’t have more recent data). Using this number with some simple statistics gives a theoretical mean time in the House almost identical to the average of those currently serving. However, the measured variance is significantly larger than the expected variance.

Now that I have a more accurate view of the makeup of congress, I can look at the reasons behind my previous misconception. The first reason is the number of times I have heard politicians and others talk about the need for term limits. The exaggerated view of careerism is reinforced by the fact that much of the congressional leadership has been in office for years. Since they are the ranking members, they appear to be disproportionately represented in national news stories. The fact that Indiana has only had three senators since I have lived here, and my House district has been misrepresented by Mark Souder since 1995, contribute to the appearance of a permanent congress.

This leads to the question of what should be done. The problem clearly isn’t as bad as I originally expected, but is it really a problem? A year or two ago, I realized that overly strict term limits for the Senate would undermine the purpose of having a bicameral legislature. But what about the House? There is evidence that strict term limits can create new problems. For now, I think that term limits in the Senate are unimportant, and I am undecided about the House. I’ll stick to my general rule of voting against incumbents that aren’t significantly better than their opponent. One final point to remember:

The founding fathers, by the way, did give us the best system of term limits there is. If you don’t like what they do, vote ’em out.
–Jack Lessenberry

Suggested reading:

• Throw All The Bums Out? Bad Idea by Tom Schaller on FiveThirtyEight
• The Entrenching of Incumbency: Reelections in the U.S. House of Representatives, 1790-1994 by Stephen C. Erickson in the Cato Journal. Being a Cato Institute publication, this talks about time in office tending to corrupt, but ignores other sources of corruption. Erickson writes about politicians bowing to special interests to be reelected, but ignores the role of special interests in getting them elected in the first place.
• Legislators and Administrators: Complex Relationships Complicated by Term Limits by Sarbaugh-Thompson et alli. Legislative Studies Quarterly isn’t open access, but a number of stories report on this paper.
• What ‘Permanent Congress’? by Mickey Edwards (R-OK) in the NYTimes. It is interesting how opinions shift according to which party has a majority.
• Reelection rates of incumbents By David C. Huckabee. This is where I found the reelection rate.

Future problems:

• Look at the age of representatives during their first term. A large portion of the drop off could be from retirement.
• Look at the careers of legislators before and after their time in congress.
• Look at how being chosen for appointed offices (e.g. the Cabinet) change the numbers.

With the TV and newspapers constantly referencing medal counts, I thought it would be interesting to come up with a good measure of how well each country performed. The problem with medal counts is that it gives an advantage to large countries that enter a number of athletes. I am much more impressed when a small or poor country enters a couple athletes who perform better than expected than I am by professional athletes from larger countries. One way create a combined score would be to give 3 points for gold, 2 for silver, 1 for bronze, then add the points up by country and divide by the number of athletes from that country. A better way would be something like:

Where:
n == number of athletes in an event
a_p == the finishing rank of an athlete (1 = gold)
a == the number of athletes a nation entered in an event
s == all events
c_a == the number of events a nation entered

This will give an average score for each country, compensating for some countries entering more athletes. While watching a couple events, I started scraping the results from the Vancouver 2010 website. This took a longer than expected, so I never got around to doing the calculations. Since I haven’t seen the results posted as nice clean CSV files anywhere, I’ll post them for others to use. I ran out of time before including the results for curling and hockey.

Now, if only the Olympics would go back to being amateurs only…

Files:

• 2010 Winter Olympics results spreadsheets (does not include hockey and curling)

The story is based on press release from the Guttmacher Institute, an abortion advocacy group, originally a division of the Planned Parenthood Federation of America. I have no reason to doubt the published numbers, but the press release makes the mistake of over-interpreting the data to agree with predetermined conclusions. The annual change in the numbers from 2005 to 2006 isn’t large enough to draw a conclusion, yet the press release attributes the change to policies they oppose. This is what Darrell Huff would call playing up numbers, and the wording could be considered cherry-picking. This is exactly the same kind of mistake I see every slightly cool day during the summer when someone (often in the news) claims that it disproves anthropogenic global warming. While it is possible that the Guttmacher Institute’s conclusion is correct, the evidence is not yet strong enough to make a conclusion. The Guttmacher Institute’s press release presents an explanation for 1995 through 2006, leaving out an explanation of the data from 1986 to 1995. This is a problem because there is a larger unexplained peak in 1988 and the decline begins in 1989, not 1995. At the present time, without presenting stronger evidence, an equally plausible explanation is that the 2005 to 2006 change merely represents the expected annual fluctuations around a steady state, and that the slow in the decline is simply due to approaching the steady state. To make their conclusions will require a longer trend, and to explain the prior changes, not just assume the change is due to policies they oppose. It is important to remember to actually look at data and to know that the world is more complex than advocacy groups pretend.

Update 2010-02-02: A new study published in the Archives of Pediatric and Adolescent Medicine provides evidence that the Guttmacher Institute’s attribution of the changes in the abortion rate is likely incorrect. Unlike the Guttmacher Institute’s conclusion, this is published in a peer-reviewed journal. (Found through a story in the Washington Post.)

I decided to try it on several of the most common religious texts. The key requirement was that I could download them from Project Gutenberg; one of my favorite websites. A second similarity is that they are rarely studied or understood by many of their professing followers. I also tried with several other texts, but left them off the chart for simplicity.

This rule also works well for problems outside of linguistics, for example: city populations, website visits, et cetera. I plotted the frequency of hits to different pages on my website and for city sizes in the United States, and found fairly good fits.

Zipf’s Law, and later extensions, are common and useful enough that there is an [R] package for dealing with them. The package developers, Stefan Evert and Marco Baroni, posted a good introduction to Zipf’s law and its uses on the zipfR project page. Their presentation materials are also a good example of slide design.

I’ve always been annoyed when people, often athletes, say “I gave it one-hundred and ten percent,” or something along those lines. Now, there are plenty of times when percentages over 100 make sense, but—by definition—your best is 100%. Unless . . . That’s it! The athletes are giving one-hundred and ten percent of their natural ability. They are admitting to doping. Their apparent abuse of basic math is really a veiled admission to using performance-enhancing drugs. The extra ten percent is the drugs!

One of today’s headlines is “Hoosier obesity rate flat at 27.4%.” The article cites a RWJF/Trust for America’s Health report, which included this map and an interesting interactive map. The original data are from the CDC National Center for Health Statistics.

Sources:

• The Journal Gazette: Hoosier obesity rate flat at 27.4%
• Trust for America’s Health: F as in Fat 2009
• RWJF: F as in Fat 2009
• CDC: Overweight Prevalence