When Averages Mislead
Smart piece in The New York Times by sociologist Stephanie Coontz about how averages can skew what we believe -- and skew social policy in negative ways:
Averages are useful because many traits, behaviors and outcomes are distributed in a bell-shaped curve, with most results clustered around the middle and a much smaller group of outliers at the high and low ends. Knowing the average number of births in an area can help builders decide how many bedrooms are likely to be needed in new houses, and alert policy makers to a brewing fertility crisis.But averages can be misleading when a distribution is heavily skewed at one end, with a small number of unrepresentative outliers pulling the average in their direction. In 2011, for example, the average income of the 7,878 households in Steubenville, Ohio, was $46,341. But if just two people, Warren Buffett and Oprah Winfrey, relocated to that city, the average household income in Steubenville would rise 62 percent overnight, to $75,263 per household.
Outliers can also pull an average down, leading social scientists to overstate the risks of particular events.
Most children of divorced parents turn out to be as well adjusted as children of married parents, but the much smaller number who lead very troubled lives can lower the average outcome for the whole group, producing exaggerated estimates of the impact of divorce.
...But in this new paper, "The Trouble With Averages," the psychologist Anthony Mancini shows that treating the average response as if it was the normal or typical outcome can lead to bad social policy and inappropriate therapeutic responses.
...When we assume that "normal" people need "time to heal," or discourage individuals from making any decisions until a year or more after a loss, as some grief counselors do, we may be giving inappropriate advice. Such advice can cause people who feel ready to move on to wonder if they are hardhearted.
That's why so many people use the median. By its nature, the median is not affected nearly as much by extreme values.
That's why, when I was on a jury and we were voting on the size of an award, I offered to calculate the median of the votes. My vote of $1 did not pull the result down, and another juror's vote of $2 million didn't pull it up.
Karl Lembke at May 26, 2013 11:01 PM
Yes, in math and science, we have this amazing tool called the median. Perhaps if journalism majors would actually learn some math in school, they might be able to use it too!
(Not a knock against Coontz, whose books I have enjoyed.)
Astra at May 27, 2013 5:53 AM
There are other issues here.
The first I can think of is that the response to an event, such as a tragedy affecting a group, is unfairly biased due to the provider's need to be seen doing something useful. Sometimes this is personal, sometimes political.
The next is that the public's perception of an "average" can be in error. For instance, gender is not binary, but social policy assumes that men are "straight", that this is determined by outward physical appearance, that they have x libido, and that only willful misbehavior can deviate from this. Some are so adamant about this that they insist that they can point at an individual born in the USA and suggest that they be denied rights.
Radwaste at May 27, 2013 6:03 AM
Another area that this can hurt is if an educator grades on a bell curve, especially in a hard subject. The student that understands the subject perfectly and gets the test right every time means the average students end up with lower grades.
Jim P. at May 27, 2013 7:24 AM
Another area that this can hurt is if an educator grades on a bell curve, especially in a hard subject. The student that understands the subject perfectly and gets the test right every time means the average students end up with lower grades.
Posted by: Jim P. at May 27, 2013 7:24 AM
Well, grading on a bell curve kinda became pointless when the goal of almost all of the educational establishment became to forget about any education, and start rolling out diplomas, no matter how stupid, lazy or unmotivated the students were.
The educators collected their salary and bonuses based on the numbers, not the achievement.
Isab at May 27, 2013 9:05 AM
Yes, in math and science, we have this amazing tool called the median.
Don't forget the mode. And that whole ANOVA thing.
ANOVA = ANalysis Of VAriance. Because sometimes the mean, mode and median are boring, and the exiciting stuff happens in the outliers.
I R A Darth Aggie at May 27, 2013 10:34 AM
A good example I saw a few years ago was little electronic widget boards. A lot failed in the first month of operation but then very few failed until the board was about six years old. Almost all had died by 8 years. The average age at failure was around 2.5 years. There was a suggestion that all the boards be replaced at 2 years. This did not make sense because if the board had lived to 2 years it almost assuredly would make it to six - so was unlikely to fail, unlike a new board.
I suppose the biggest difficulty was that over the years the board quality varied as the process was improved,etc.
The Former Banker at May 27, 2013 11:41 AM
Amy Alkon
http://www.advicegoddess.com/archives/2013/05/27/when_averages_m.html#comment-3722578">comment from I R A Darth AggieThe ANOVA is important. It's why it's important to read a study instead of just looking at the conclusions in the media.
Amy Alkon
at May 27, 2013 12:46 PM
Proof that people slept through statistics class, if they took it at all. Not all distributions are normal and the descriptive statistics that work well for normal distributions do not apply.
People who are ready to move on are the other type of normal - the kind we used to have until everyone went all Oprah on us. That's life. Nobody gets out alive, and fair is something you go to in the summer.
MarkD at May 28, 2013 4:30 AM
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