Range Of Error
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engineering, see Tolerance (engineering). For the eponymous movie, see Margin for error (film). The top portion charts probability density against actual percentage, showing the relative probability that the actual percentage is realised, based on the sampled percentage. In the bottom
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portion, each line segment shows the 95% confidence interval of a sampling (with the margin margin of error confidence interval calculator of error on the left, and unbiased samples on the right). Note the greater the unbiased samples, the smaller the margin of margin of error definition error. The margin of error is a statistic expressing the amount of random sampling error in a survey's results. It asserts a likelihood (not a certainty) that the result from a sample is close to the number one
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would get if the whole population had been queried. The likelihood of a result being "within the margin of error" is itself a probability, commonly 95%, though other values are sometimes used. 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. Margin of error applies whenever a population is incompletely sampled. Margin of
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error is often used in non-survey contexts to indicate observational error in reporting measured quantities. In astronomy, for example, the convention is to report the margin of error as, for example, 4.2421(16) light-years (the distance to Proxima Centauri), with the number in parentheses indicating the expected range of values in the matching digits preceding; in this case, 4.2421(16) is equivalent to 4.2421 ± 0.0016.[1] The latter notation, with the "±", is more commonly seen in most other science and engineering fields. Contents 1 Explanation 2 Concept 2.1 Basic concept 2.2 Calculations assuming random sampling 2.3 Definition 2.4 Different confidence levels 2.5 Maximum and specific margins of error 2.6 Effect of population size 2.7 Other statistics 3 Comparing percentages 4 See also 5 Notes 6 References 7 External links Explanation[edit] The margin of error is usually defined as the "radius" (or half the width) of a confidence interval for a particular statistic from a survey. One example is the percent of people who prefer product A versus product B. 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. If the statistic is a percentage, this maximum margin of error can be calculated as the radius of the confidence interval for a
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Acceptable Margin Of Error
Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Margin of Error In a confidence interval, the margin of error synonym range of values above and below the sample statistic is called the margin of error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design https://en.wikipedia.org/wiki/Margin_of_error to ensure that our sample estimate will not differ from the true population value by more than, say, 5 percent (the margin of error) 90 percent of the time (the confidence level). How to Compute the Margin of Error The margin of error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value http://stattrek.com/estimation/margin-of-error.aspx?Tutorial=AP x Standard error of the statistic If you know the standard deviation of the statistic, use the first equation to compute the margin of error. Otherwise, use the second equation. Previously, we described how to compute the standard deviation and standard error. How to Find the Critical Value The critical value is a factor used to compute the margin of error. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal. The central limit theorem states that the sampling distribution of a statistic will be nearly normal, if the sample size is large enough. As a rough guide, many statisticians say that a sample size of 30 is large enough when the population distribution is bell-shaped. But if the original population is badly skewed, has multiple peaks, and/or has outliers, researchers like the sample size to be even larger. When the sampling distribution is nearly normal, the critical value can be expressed as a t score or as a z score. When the sample size is smaller, the critical value should only be expressed as a t statistic. To find the critical value, follow these steps. Compute alpha (α): α = 1 - (confidence level / 10
Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Wed Oct 19 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Probability http://mathworld.wolfram.com/MarginofError.html and Statistics>Error Analysis> History and Terminology>Disciplinary Terminology>Political Terminology> MathWorld Contributors>Pegg> Margin of Error http://www.robertniles.com/stats/margin.shtml The margin of error is an estimate of a confidence interval for a given measurement, result, etc. and is frequently cited in statistics. While phrases such as, "The poll has a margin of error of plus or minus 3.1 percentage points" are commonly heard, an additional qualification such as "at a of error 95 percent confidence level" is also needed in order to precisely indicate what the error refers to. For a given confidence interval , standard deviation , and sample size , the margin of error (for a normal distribution) is where is the inverse erf function. SEE ALSO: Confidence Interval, Error, Inverse Erf, Standard Deviation Portions of this entry contributed by Ed Pegg, Jr. (author's link) margin of error REFERENCES: Moore, D.S. and McCabe G.P. Introduction to the Practice of Statistics. New York: W.H.Freeman, p.443, 1999. Referenced on Wolfram|Alpha: Margin of Error CITE THIS AS: Pegg, Ed Jr. and Weisstein, Eric W. "Margin of Error." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MarginofError.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Computerbasedmath.org» Join the initiative for modernizing math education. Online Integral Calculator» Solve integrals with Wolfram|Alpha. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own. Wolfram Problem Generator» Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Wolfram Language» Knowledge-based programming for everyone. Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: margin of error n=1000 b
accurate, assuming you counted the votes correctly. (By the way, there's a whole other topic in math that describes the errors people can make when they try to measure things like that. But, for now, let's assume you can count with 100% accuracy.) Here's the problem: Running elections costs a lot of money. It's simply not practical to conduct a public election every time you want to test a new product or ad campaign. So companies, campaigns and news organizations ask a randomly selected small number of people instead. The idea is that you're surveying a sample of people who will accurately represent the beliefs or opinions of the entire population. But how many people do you need to ask to get a representative sample? The best way to figure this one is to think about it backwards. Let's say you picked a specific number of people in the United States at random. What then is the chance that the people you picked do not accurately represent the U.S. population as a whole? For example, what is the chance that the percentage of those people you picked who said their favorite color was blue does not match the percentage of people in the entire U.S. who like blue best? Of course, our little mental exercise here assumes you didn't do anything sneaky like phrase your question in a way to make people more or less likely to pick blue as their favorite color. Like, say, telling people "You know, the color blue has been linked to cancer. Now that I've told you that, what is your favorite color?" That's called a leading question, and it's a big no-no in surveying. Common sense will tell you (if you listen...) that the chance that your sample is off the mark will decrease as you add more people to your sample. In other words, the more people you ask, the more likely you are to get a representative sample. This is easy so far, right? Okay, enough with the common sense. It's time for some math. (insert smirk here) The formula that describes the relationship I just mentioned is basically this: The margin of error in a sample = 1 divided by the square root of the number of people in the sample How did someone