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:
- It can represent the range within which the true Statistical Population Parameter is expected to lie with a certain level of confidence.
- It can be used to gauge the reliability of results obtained through Sampling Methods.
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- 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.
- 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.
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.
- 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.
2010
- (McAfee, 2010) ⇒ Gerry McAfee. (2010). “Master Math: AP Statistics, 1st Edition.” Course Technology Ptr. ISBN:1435456270
- QUOTE: Margin of error: When dealing with a one-proportion z-interval, the margin of error is the distance from the endpoints of the confidence interval to the center of the interval, [math]\displaystyle{ pˆ }[/math]. The margin of error is the product of the z* value and the standard error and is affected primarily by the sample size and the z* value (confidence level). The margin of error for a t-interval is affected in a similar fashion by the sample size and the level of confidence.
2008
- (Upton & Cook, 2008) ⇒ Graham Upton, and Ian Cook. (2008). “A Dictionary of Statistics, 2nd edition revised." Oxford University Press. ISBN:0199541450
- QUOTE: A ‘margin of error' is often reported with opinion polls using a phrase such as ‘the proportion intending to vote for the Red party is 35%, with a margin of error of 3%.’ This actually means that on an average of 19 times out of 20, the sample proportion obtained will be within 3% of the the value of the population proportion; it is therefore defining a 95% confidence interval for the population proportion, with the margin of error amounting to half the width of that interval.z