The margin of error only takes random sampling error into account. A larger sample size produces a smaller margin of error, all else remaining equal. Along with the confidence level, the sample design for a survey, and in particular its sample size, determines the magnitude of the margin of error. This level is the probability that a margin of error around the reported percentage would include the "true" percentage. Like confidence intervals, the margin of error can be defined for any desired confidence level, but usually a level of 90%, 95% or 99% is chosen (typically 95%). This maximum margin of error can be calculated as the radius of the confidence interval for a reported percentage of 50%. When a single, global margin of error is reported for a survey, it refers to the maximum margin of error for all reported percentages using the full sample from the survey. The margin of error is usually defined as the radius of the confidence interval for a particular statistic from a survey. 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. The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the sample is, the smaller the margin of error is. In other words, one is 95% sure that the "true" percentage is in this region given a poll with the sample size shown to the right. The bottom portion of this graphic shows the margin of error, the corresponding zone of 95% confidence.
The top portion of this graphic depicts probability densities that show the relative likelihood that the "true" percentage is in a particular area given a reported percentage of 50%.
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