An estimate from a survey is unlikely to exactly equal the true population quantity of interest for a variety of reasons. For one thing, the questions maybe badly worded. For another, some people who are supposed to be in the sample may not be at home, or even if they are, they may refuse to participate or may not tell the truth. These are sources of “nonsampling error.”
But the estimate will probably still differ from the true value, even if all nonsampling errors could be eliminated. This is because data in a survey are collected from only some—but not all—members
of the population to make data collection cheaper or faster, usually both.
of the population to make data collection cheaper or faster, usually both.
Of course, just by chance, a majority in a particular sample might support Ms. Smith even if the majority in the population supports Mr. Jones. Such an occurrence might arise due to “sampling
error,” meaning that results in the sample differ from a target population quantity, simply due to the “luck of the draw”—i.e., by which set of 100 people were chosen to be in the sample.
error,” meaning that results in the sample differ from a target population quantity, simply due to the “luck of the draw”—i.e., by which set of 100 people were chosen to be in the sample.
Does sampling error render surveys useless? Fortunately, the answer to this question is “No.” But how should we summarize the strength of the information in a survey? That is a role for the margin of error.
The “margin of error” is a common summary of sampling error, referred to regularly in the media,
which quantifies uncertainty about a survey result. The margin of error can be interpreted by making use of ideas from the laws of probability or the “laws of chance,” as they are sometimes called.
which quantifies uncertainty about a survey result. The margin of error can be interpreted by making use of ideas from the laws of probability or the “laws of chance,” as they are sometimes called.
Such intervals are sometimes called 95% confidence intervals and would be expected to contain the true value at least 95% of the time.
Larger samples are more likely to yield results close to the target population quantity and thus have smaller margins of error than more modest-sized samples.
In the case of the mayoral poll in which 55 of 100 sampled individuals support Ms. Smith, the sample estimate would be that 55 percent support Ms. Smith—however, there is a margin of error of 10 percent. Therefore, a 95 percent confidence interval for the percentage supporting Ms. Smith would be (55%-10%) to (55%+10%) or (45 percent, 65 percent), suggesting that in the broader community the support for Ms. Smith could plausibly range from 45 percent to 65 percent.