Margin of Error Statistic

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A Margin of Error Statistic is a sampling statistic that quantifies the level of uncertainty / random sampling error in an estimated value.

  • Context:
  • Example(s):
    • In a political poll, 60% of surveyed voters support a particular candidate and the margin of error is reported as +/- 3%. This means that the true proportion of support is likely to fall between 57% and 63%.
    • In medical research, a drug is found to be 90% effective with a margin of error of 5%. This implies that the drug's effectiveness can range between 85% and 95%.
    • ...
  • Counter-Example(s):
    • Standard Deviation: Measures the dispersion or spread of a set of values, but does not directly indicate the accuracy or reliability of a single estimate.
    • Coefficient of Variation: A normalized measure of the dispersion of a probability distribution. It does not offer a range within which a population parameter is likely to lie.
    • P-Value: Used in hypothesis testing to indicate the probability of observing a test statistic as extreme as the one computed from the sample data. It is not a measure of uncertainty around a specific estimate.
    • R-Squared Value: In regression analysis, indicates the proportion of the variance for the dependent variable that's explained by independent variables in the model. It does not give a range of uncertainty around a specific point estimate.
    • ...
  • See: Observational Error, Sampling Error, Statistical Survey, Statistical Population, Variance, Confidence Interval, Z-Score, Sample Size, Level of Confidence.


References

2023

  • (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Margin_of_error Retrieved:2023-10-4.
    • The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a census of the entire population. The margin of error will be positive whenever a population is incompletely sampled and the outcome measure has positive variance, which is to say, whenever the measure varies.

      The term margin of error is often used in non-survey contexts to indicate observational error in reporting measured quantities.

2023

  • GBard
    • A margin of error statistic is a sampling statistic that expresses the amount of random sampling error in the results of a survey. It is calculated using a confidence level and the sample size. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a census of the entire population.

      The margin of error is used to construct a confidence interval, which is a range of values that is likely to contain the true population value. For example, if a poll finds that 52% of voters support a particular candidate, with a margin of error of 3%, then we can be 95% confident that the true percentage of voters who support the candidate is between 49% and 55%.

    • Example: A poll of 1,000 voters finds that 52% support a particular candidate. The margin of error for the poll is calculated to be 3%. This means that we can be 95% confident that the true percentage of voters who support the candidate is between 49% and 55%.
      The margin of error is an important statistic to consider when interpreting the results of a survey. It can help us to understand how much confidence we can have in the results, and how likely it is that the results will be different if the survey is repeated.

2010

2008