Definition Standard Error Proportion
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proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above and below the actual value. The standard error (SE) standard error of proportion formula is the standard deviation of the sampling distribution of a statistic,[1] most
Standard Error Proportion Calculator
commonly of the mean. The term may also be used to refer to an estimate of that standard standard error of proportion in r deviation, derived from a particular sample used to compute the estimate. For example, the sample mean is the usual estimator of a population mean. However, different samples drawn from that standard error of proportion difference same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and variance). The standard error of the mean (SEM) (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples
Standard Error Of Proportion Sample
(of a given size) drawn from the population. Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time. In regression analysis, the term "standard error" is also used in the phrase standard error of the regression to mean the ordinary least squares estimate of the standard deviation of the underlying errors.[2][3] Contents 1 Introduction to the standard error 1.1 Standard error of the mean 1.1.1 Sampling from a distribution with a large standard deviation 1.1.2 Sampling from a distribution with a small standard deviation 1.1.3 Larger sample sizes give smaller standard errors 1.1.4 Using a sample to estimate the standard error 2 Standard error of the mean 3 Student approximation when σ value is unknown 4 Assumptions and usage 4.1 Standard error of mean versus standard deviation 5 Correction for finite population 6 Correction for correlation in the sample 7 Relative standard error 8 See also 9 References Introduction to the standard error[edit] The standard error is a quantitative measure
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Margin Of Error Proportion
Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends What is the Standard https://en.wikipedia.org/wiki/Standard_error Error? The standard error is an estimate of the standard deviation of a statistic. This lesson shows how to compute the standard error, based on sample data. The standard error is important because it is used to compute other measures, like confidence intervals and margins of error. Notation The following notation http://stattrek.com/estimation/standard-error.aspx?Tutorial=AP is helpful, when we talk about the standard deviation and the standard error. Population parameter Sample statistic N: Number of observations in the population n: Number of observations in the sample Ni: Number of observations in population i ni: Number of observations in sample i P: Proportion of successes in population p: Proportion of successes in sample Pi: Proportion of successes in population i pi: Proportion of successes in sample i μ: Population mean x: Sample estimate of population mean μi: Mean of population i xi: Sample estimate of μi σ: Population standard deviation s: Sample estimate of σ σp: Standard deviation of p SEp: Standard error of p σx: Standard deviation of x SEx: Standard error of x Standard Deviation of Sample Estimates Statisticians use sample statistics to estimate population parameters. Naturally, the value of a statistic may vary from one sample to the next. The variability of a statistic
on the Mean Learning Objectives Estimate the population proportion from sample proportions Apply the correction for continuity Compute a confidence interval A candidate in a two-person http://onlinestatbook.com/2/estimation/proportion_ci.html election commissions a poll to determine who is ahead. The pollster randomly chooses 500 registered voters and determines that 260 out of the 500 favor the candidate. http://www.stat.wmich.edu/s216/book/node70.html In other words, 0.52 of the sample favors the candidate. Although this point estimate of the proportion is informative, it is important to also compute a confidence standard error interval. The confidence interval is computed based on the mean and standard deviation of the sampling distribution of a proportion. The formulas for these two parameters are shown below: μp = π Since we do not know the population parameter π, we use the sample proportion p as an estimate. The estimated standard error of standard error of p is therefore We start by taking our statistic (p) and creating an interval that ranges (Z.95)(sp) in both directions, where Z.95 is the number of standard deviations extending from the mean of a normal distribution required to contain 0.95 of the area (see the section on the confidence interval for the mean). The value of Z.95 is computed with the normal calculator and is equal to 1.96. We then make a slight adjustment to correct for the fact that the distribution is discrete rather than continuous.
Normal Distribution Calculator sp is calculated as shown below: To correct for the fact that we are approximating a discrete distribution with a continuous distribution (the normal distribution), we subtract 0.5/N from the lower limit and add 0.5/N to the upper limit of the interval. Therefore the confidence interval is Lower limit: 0.52 - (1.96)(0.0223) - 0.001 = 0.475 Upper limit: 0.52 + (1.96)(0.0223) + 0.001 = 0.565 0.475 ≤ π ≤ 0.565 Sinpopulation parameters like p are typically unknown and estimated from the data. Consider estimating the proportion p of the current WMU graduating class who plan to go to graduate school. Suppose we take a sample of 40 graduating students, and suppose that 6 out of the 40 are planning to go to graduate school. Then our estimate is of the graduating class plan to go to graduate school. Now is based on a sample, and unless we got really lucky, chances are the .15 estimate missed. By how much? On the average, a random variable misses the mean by one SD. From the previous section, the SD of equals . It follows that the expected size of the miss is . This last term is called the standard error of estimation of the sample proportion, or simply standard error (SE) of the proportion . However, since we do not know p, we cannot calculate this SE. In a situation like this, statisticians replace p with when calculating the SE. The resulting quantity is called the estimated standard error of the sample proportion . In practice, however, the word ``estimated'' is dropped and the estimated SE is simply called the SE . Exercise 4. a. If 6 out of 40 students plan to go to graduate school, the proportion of all students who plan to go to graduate school is estimated as ________. The standard error of this estimate is ________. b. If 54 out of 360 students plan to go to graduate school, the proportion of all students who plan to go to graduate school is estimated as ________. The standard error of this estimate is ________. Exercise 4 shows the effect of of increasing the sample size on the SE of the sample proportion. Multiplying the sample size by a factor of 9 (from 40 to 360) makes the SE decrease by a factor of 3. In the formula for the SE of , the sample size appears (i) in the denominator, and (ii) inside a squareroot. Therefore, multiplying the sample size by a certain factor divides the SE of by the squareroot of that factor Next: Exercises Up: Sampling Distribution of the Previous: The Sampling Distribution of 2003-09-08