The margin of error is a measure that determines the representativeness
of a sample by comparing the number of respondents in the sample to the
number of people in the population. The opinions expressed by respondents
in a sample are an estimate of the opinions held by all people within the
target population. The opinions expressed in a sample are estimates because
the only way to truly measure the opinions of the whole population would
be to interview each individual in the population. Generally, as sample
size increases the margin of error decreases. Therefore, as the sample size
increases, the opinions measured in the sample will be closer to those within
the actual population.
Through accepted mathematical formulas, confidence level and margin of error
are calculated. For example, a margin of error of +4.9 percent at the 95
percent confidence level means that if 40 percent of the respondents answer
"yes" to a question, we can be 95 percent confident that the actual
value in the population to this question is 4.9 percentage points higher
or lower than 40 percent. In other words, the actual range falls between
35.1 percent and 44.9 percent. This range is referred to as the "confidence
interval." Some other examples at the 95 percent confidence level are
presented below:
Target Population |
Sample Size |
Margin of Error |
Proportion of Population |
100,000 |
800 |
± 3.5 |
0.8% |
100,000 |
500 |
± 4.4 |
0.5% |
1,000 |
400 |
± 3.8 |
40% |
1,000 |
300 |
± 4.7 |
30% |
800 |
300 |
± 4.5 |
38% |
800 |
200 |
± 6.0 |
25% |
500 |
300 |
± 3.6 |
60% |
500 |
200 |
± 5.4 |
40% |
This level of confidence requires a sample size large enough that if the same survey were conducted 100 times with a random sample, only five of the surveys would be expected to yield results outside the margin of error.
