Monday night, Stephen Colbert interviewed a sexy mathematician, so it was disappointing to see the very first moments of Jon Stewart’s show the next evening succumb to some terrible, horrible, no good, very bad math.
It all started when Stewart aired part of an interview featuring Secretary of Health and Human Services Kathleen Sebelius speaking about Obamacare, way back in September 2013:
I think success looks like at least 7 million people having signed up by the end of March 2014.
As you may have heard, the end of March 2014 has now come and gone, and Barack Obama immediately took to the airwaves to proclaim that his program had not only met, but exceeded the goals it set at the outset:
7.1 million Americans have now signed up for private insurance plans through these marketplaces. 7.1.
Wow. You got it almost exactly. With a healthy 1.4% margin of error. That will ease suspicions.
Where did Stewart get that 1.4% margin of error?
Well, it’s possible he is giving us new information about the size of the sample and its distribution, which he used to calculate said margin.
But it seems much more likely that Stewart is simply misusing the term “margin of error.” My suspicions arise from noting the following happy “coincidence”: 100,000 divided by 7,100,000 multiplied by 100 equals 1.408% — I suppose Leibowitz would call that 1.4% with a .008% margin of error… except that “the difference between the figure you expected and the figure you actually observed” is not at all what margin of error means!
Here’s Wikipedia, in case you don’t believe me:
The margin of error is a statistic expressing the amount of random sampling error in a survey’s results. The larger the margin of error, the less confidence one should have that the poll’s reported results are close to the “true” figures; that is, the figures for the whole population. Margin of error occurs whenever a population is incompletely sampled.
The more you know.
For all the crap Stewart gave Nate Silver last week, look who is spreading misinformation and ignorance now?