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.’

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.

The number of miles driven in a year decreases with the age of a car:

I combined these two equations to find the percentage of all miles driven in a year for cars by age. The combination of these two factors decreases more rapidly than either alone:

Even in the period where most cars for a model year are on the road, the number of miles the older cars are driven decreases. This means the average fuel economy for all cars on the road has very little hysteresis for changes in the average economy of new cars. Basically, the average fuel economy of all cars on the road will be close to the fuel economy of the current model year. The numbers for light trucks (all pickups and most SUVs) are similar. This means that any changes to fuel economy standards, or the popularity of SUVs versus cars, will quickly change the total gasoline consumption for the country.

UPDATE (20090129): What this directly shows is the percent of total distance for a model year driven by car age. If the same number of cars are built each year, the results also work for all cars on the road. If fewer cars than average are built, the delay will be a little longer. If more are built, the delay will be shorter.

I saw a graph of car and bicycle production in The Economist. The article was On your bike: Obesity and high oil prices are good news for the world’s biggest bikemaker. This was one of the many recent stories on the increase in gas prices leading to more people riding bikes. The graph looks something like this:

Bicycle and car production (1950--2007)

Car production is increasing as expected, but bike production is even higher. But does this plot tell us anything useful? Doesn’t world population growth look similar? I found that world population looks like this:

World population (1950--2007)

This is a huge increase. To make the bicycle production plot more useful, I can find the per capita production. Just divide the production by population:

Per capita car and bicycle production (1950--2007)

This is a much more useful plot. Bicycle production is going up, but not as fast in the original graph. The current production is actually slightly lower per capita than in the late ’80s. The flatness of the car production line is surprising. I also added a five year moving average to the plot.

Since there are so many articles linking bicycling to gas prices, lets look at the price of gasoline. Because of inflation and other factors, the absolute price of gas isn’t very useful. I found the consumer price index adjusted gas price:

US CPI adjusted gasoline prices (1950--2007)

Hmm… that doesn’t look as bad as you would expect. This graph does make it really obvious that the data I am using stops in 2007. I can now add the gas price to the production plot. The production scale is on the left, the price scale is on the right:

CPI adjusted gas prices and global car and bicycle production (1950--2007)

Interesting. The gas price and bike production don’t match at all before the mid ’90s. The match for the past ten or so years is pretty good.

These are just some thoughts on getting useful information from graphs. I didn’t do any actual statistics, but this gives some ideas for how to make these plots more useful.

I highly recommend reading How to Lie with Statistics by Darrel Huff.

Sources:

• The Economist: On your bike: Obesity and high oil prices are good news for the world’s biggest bikemaker
• Earth Policy Institute: Economic Indicators: Bicycles
• U.S. Census Bureau: International Database
• U.S. DOE Energy Information Administration: Peal Petroleum Prices