Convert Standard Error To Margin Of Error
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Confidence Interval Margin Of Error
Anybody can answer The best answers are voted up and rise to the top What is the difference between “margin of error” and “standard error”? up vote 9 down vote favorite 4 Is "margin of error" the same as "standard error"? A (simple) example to illustrate the difference would be great! definition share|improve this question edited Sep 23 '11 at 18:04 whuber♦ 145k17280540 asked Sep 23 '11 at how is margin of error calculated in polls 17:06 Adhesh Josh 90783256 add a comment| 3 Answers 3 active oldest votes up vote 13 down vote accepted Short answer: they differ by a quantile of the reference (usually, the standard normal) distribution. Long answer: you are estimating a certain population parameter (say, proportion of people with red hair; it may be something far more complicated, from say a logistic regression parameter to the 75th percentile of the gain in achievement scores to whatever). You collect your data, you run your estimation procedure, and the very first thing you look at is the point estimate, the quantity that approximates what you want to learn about your population (the sample proportion of redheads is 7%). Since this is a sample statistic, it is a random variable. As a random variable, it has a (sampling) distribution that can be characterized by mean, variance, distribution function, etc. While the point estimate is your best guess regarding the population parameter, the standard error is your best guess regarding the standard deviation of your estimator (or, in some cases, the square root of the mean squared error, MSE = bias$^2$ + variance). For a sample of size $n=1000$, the standard error of your proportion estimate is $\sqrt{0.07\c
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Margin Of Error Sampling Error
and solutions Formulas Notation Share with Friends Margin of Error In a confidence interval, the range of values above and below the
Standard Error Sample Size
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 to ensure that our sample estimate will not differ http://stats.stackexchange.com/questions/15981/what-is-the-difference-between-margin-of-error-and-standard-error 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 x Standard error of the statistic If you know the standard deviation of http://stattrek.com/estimation/margin-of-error.aspx 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 / 100) Find the critical probability (p*): p* = 1 - α/2 To express the critical value as a z score, find the z score having a cumulative p
Curve) Z-table (Right of Curve) Probability and Statistics Statistics Basics Probability Regression Analysis Critical Values, Z-Tables & Hypothesis Testing Normal Distributions: Definition, Word Problems T-Distribution Non Normal Distribution Chi Square Design of Experiments Multivariate Analysis Sampling http://www.statisticshowto.com/how-to-calculate-margin-of-error/ in Statistics Famous Mathematicians and Statisticians Calculators Variance and Standard Deviation Calculator Tdist Calculator Permutation Calculator / Combination Calculator Interquartile Range Calculator Linear Regression Calculator Expected Value Calculator Binomial Distribution Calculator Statistics Blog Calculus Matrices http://crab.rutgers.edu/~goertzel/marginsoferror.htm Practically Cheating Statistics Handbook Navigation How to Calculate Margin of Error in Easy Steps Probability and Statistics > Critical Values, Z-Tables & Hypothesis Testing > How to Calculate Margin of Error Contents (click to skip margin of to that section): What is a Margin of Error? How to Calculate Margin of Error (video) What is a Margin of Error? The margin of error is the range of values below and above the sample statistic in a confidence interval. The confidence interval is a way to show what the uncertainty is with a certain statistic (i.e. from a poll or survey). For example, a poll might state that there margin of error is a 98% confidence interval of 4.88 and 5.26. That means if the poll is repeated using the same techniques, 98% of the time the true population parameter (parameter vs. statistic) will fall within the interval estimates (i.e. 4.88 and 5.26) 98% of the time. What is a Margin of Error Percentage? A margin of error tells you how many percentage points your results will differ from the real population value. For example, a 95% confidence interval with a 4 percent margin of error means that your statistic will be within 4 percentage points of the real population value 95% of the time. The Margin of Error can be calculated in two ways: Margin of error = Critical value x Standard deviation Margin of error = Critical value x Standard error of the statistic Statistics Aren't Always Right! The idea behind confidence levels and margins of error is that any survey or poll will differ from the true population by a certain amount. However, confidence intervals and margins of error reflect the fact that there is room for error, so although 95% or 98% confidence with a 2 percent Margin of Error might sound like a very good statistic, room for error is built in, which means sometimes statistics are w
need the margin of error for a mean score or for a percentage. If it is a mean score (an average of a continuous variable, e.g., income in dollars, test score points, pounds, inches, etc.), skip to the end of the page and use Formula Four. If you are dealing with percentages, you must choose among three formulas depending on the information given and requested in the question (if you are not told that it is a mean or average, assume that percentages will be computed): y ou are told only the size of the sample and are asked to provide the margin of error for percentages which are not (yet) known. This is typically the case when you are computing the margin of error for a survey which is going to be conducted in the future. It is also useful for getting a general "ballpark" figure for a sample as a whole. In this case, you use Formula One. You are given a percentage result, e.g., 65% voted for Candidate Blowhard. In this case you use Formula Two. You are told the margin of error which is acceptable, and asked to compute the sample size. In this case you use Formula Three. If not told otherwise, assume that any question which asks for a sample size wants a margin of error for percentages. Formula One: This is the easy one, you should try to learn to use it in your head: M = 1/SQRT(N). Caution: N refers to the sample which answered the question at hand, e.g., if you are asked for the margin of error for the Hispanic respondents, N refers to the number of Hispanics in the sample. The answers will be in proportions, to get percents move the decimal point two digits to the right. The confidence interval is + or - M. Thus if M = .04, the confidence interval is +/- 4%. Formula Two: In this formula, "p" refers to the proportion (not the percentage) giving a certain answer to a question. For example, if 65% voted for Blowhard, p = .65. N, as always, refers to the sample which answered the question at hand. M = 2 * SQRT((p * (1-p))/N). You must do this calculation in the proper order. First determine p and 1-p. If p = .65, for example, 1-p means 1-.65 or .35. Then multiply p times 1-p, divide the result by N, take the square root and multiply the result by 2 (or 1.96 if you are a perfectionist). This is best done as a chain calculation in your calculator, without writing any of the intermediate steps down. To get confidence intervals, take p and add M to get the upper bound, subtract M to get the lower bound. It is conventional to use per