Test your understanding: Margin of Error

Today in lecture I touched on margin of error. I want to make sure this was clear because it will be on your next exam. Below are two examples of interpreting margin of error.

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--Example 1--

According to a recent Globe and Mail poll, 70% of Torontonians would vote Liberal if a federal election were help today.  The poll surveyed 500 people living in Toronto on February 3 with a margin of error of 5 percentage points.  It’s considered accurate 19 times out of 20.

1. Interpret the margin of error.

If given again, the same poll would have results within plus or minus 5 points of 70 percent (or between 65-75%) 19 times out of 20.  Only 1/20 polls would have results outside the 65-75% margin of error.

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--Example 2--

OTTAWA—The Conservatives, hit by bad publicity in the wake of Stephen Harper’s second effort to suspend Parliament, have slipped against the Liberals in a new poll released Monday but still maintain a 6 percentage point lead.

The CBC poll taken February 8 of 1095 registered voters showed the Conservatives would maintain their minority government if an election were held now.  Public support for the Conservatives is 43%, with the Liberals 37%, NDP 9%, the Bloc trailing at 7%, and 4% of voters undecided.  The poll has a margin of error of plus or minus four percentage points 95/100.

A similar poll on January 11 showed the Conservatives with 46% support, Liberals 34%, NDP 14% and Bloc 6%.

1.  What is the margin of error?

Plus or minus 4 percentage points 95/100 times.  For every 100 polls of the same question, results for 95 will be within 4 points.  Put another way, only 5/100 (or 1/20) polls will be completely off-the-wall different!

2.  Is there reasonable statistical basis for claiming that favorability for the Conservatives has declined?

No, statistically there is no change.  If you gave this poll 100 times, 95 of those times the percentage of people giving a particular answer would be within 4 percentage points of this poll.  The percentage of people in the latest poll who say they support the Conservatives is within 4 percentage points of those who said they supported them in the previous poll (43-46%) and the same goes for the Liberals.  Therefore the Liberals have made up no measurable ground on the Conservatives.

3.  What conclusions can be drawn?

There results are more or less consistent.  If anything, support for the NDP has measurably dropped.