Do your students struggle to understand the meaning of a margin of error in polls?  The New York Times' The Upshot created a helpful illustration, using US job reports as an example.  Every month,  the Bureau of Labor Statistics, which is part of the Labor Department, conducts a large survey of 144,000 employers in order to assess how many jobs there are in the United States.  This job report is an important tool to evaluate the health of the economy.

And yet, as this Upshot article explains, one should not put too much stock in these figures:

"Even with all those survey participants, there is sampling error; the employers responding to the survey might be different from the nation's employers as a whole. And the Labor Department's initial release, coming as it does so soon after the survey, is released before all the data is in, with researchers filling in the gaps with statistical estimates that might prove wrong. Only in later weeks and months is all the data available, and the bureau then revises its initial numbers."

In addition,

"The sampling error becomes magnified because those of us following the jobs report don't focus on the total number of jobs in the economy (more than 130 million). We focus on the relatively small change in the number of these jobs from month to month (typically a few hundred thousand, at most)."

To illustrate how statistical noise might affect our perception of job trends, the Upshot created a computer simulation that assumes that "the economy is adding exactly 150,000 jobs every month, and that the monthly estimates of job growth come with exactly as much statistical noise as the Labor Department says its estimates have."

In this scenario job growth is steady, which should look like the chart below on the left--a straight line.  However, sampling error introduces statistical noise that can make the chart look like the chart below on the right.

A second scenario posited accelerating job growth (true job growth starts at 150,000 jobs in January and accelerates by 15,000 a month through December).  As the chart below demonstrates, statistical noise can make it difficult to make out this pattern in the data.  "Month by month, you wouldn't have any way of knowing if it was a true acceleration, or just a false signal generated by sampling error."



Read more:
http://www.nytimes.com/2014/05/02/upshot/how-not-to-be-misled-by-the-jobs-report.html?abt=0002&abg=1
http://www.bls.gov/

TeachingwithData.org resources:
Dancing statistics: explaining the statistical concept of sampling & standard error through dance (http://www.teachingwithdata.org/resource/3910)
Bureau of Labor Statistics: Databases, Tables & Calculators by Subject (http://www.teachingwithdata.org/resource/3886)
Economy Track: Employment to Population Ratio (http://www.teachingwithdata.org/resource/2936)