# How To Reduce The Standard Error

Example | Discussion | See also Description If you measure a sample from a wider population, then the average (or mean) of the sample will be an approximation of the population mean. But how accurate is this? how does sample size effect standard deviation If you measure multiple samples, their means will not all be the same, and will how to reduce standard deviation by half be spread out in a distribution (although not as much as the population). Due to the central limit theorem, the means will be

## What Is Standard Error

spread in an approximately Normal, bell-shaped distribution. The standard error, or standard error of the mean, of multiple samples is the standard deviation of the sample means, and thus gives a measure of their spread. Thus 68% of

## Standard Error Calculator

all sample means will be within one standard error of the population mean (and 95% within two standard errors). What the standard error gives in particular is an indication of the likely accuracy of the sample mean as compared with the population mean. The smaller the standard error, the less the spread and the more likely it is that any sample mean is close to the population mean. A small standard error is thus a Good Thing. standard error vs standard deviation When there are fewer samples, or even one, then the standard error, (typically denoted by SE or SEM) can be estimated as the standard deviation of the sample (a set of measures of x), divided by the square root of the sample size (n): SE = stdev(xi) / sqrt(n) Example This shows four samples of increasing size. Note how the standard error reduces with increasing sample size. Sample 1 Sample 2 Sample 3 Sample 4 9 6 5 8 2 6 3 1 1 8 6 7 8 4 1 3 7 3 8 2 3 6 4 9 7 7 1 1 8 1 9 7 9 3 1 6 8 3 4 Mean: 4.00 6.50 4.83 4.78 Std dev, s: 4.36 1.97 2.62 2.96 Sample size, n: 3 6 12 18 sqrt(n): 1.73 2.45 3.46 4.24 Standard error, s/sqrt(n): 2.52 0.81 0.76 0.70 Discussion The standard error gives a measure of how well a sample represents the population. When the sample is representative, the standard error will be small. The division by the square root of the sample size is a reflection o

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## Sampling Distribution Of The Mean

Us Learn more about Stack Overflow the company Business Learn more about hiring confidence interval calculator developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question margin of error and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask http://changingminds.org/explanations/research/statistics/standard_error.htm a question Anybody can answer The best answers are voted up and rise to the top Why does the standard deviation not decrease when I do more measurements? [duplicate] up vote 11 down vote favorite 6 This question already has an answer here: Difference between standard error and standard deviation 4 answers I made 100 measurements of a certain quantity, calculated mean and standard deviation (with MySQL), http://stats.stackexchange.com/questions/89456/why-does-the-standard-deviation-not-decrease-when-i-do-more-measurements and got mean=0.58, SD=0.34. The std seemed too high relative to the mean, so I made 1000 measurements. This time I got mean=0.572, SD=0.33. I got frustrated by the high standard deviation, so I made 10,000 measurements. I got mean=0.5711, SD=0.34. I thought maybe this was a bug in MySQL, so I tried to use the Excel functions, but got the same results. Why does the standard deviation remain high even though I do so many measurements? standard-deviation experiment-design share|improve this question edited Mar 11 '14 at 5:14 Jeromy Anglim 27.7k1394197 asked Mar 10 '14 at 14:03 Erel Segal-Halevi 4041313 marked as duplicate by Nick Cox, Glen_b♦, whuber♦ Mar 11 '14 at 12:00 This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. add a comment| 3 Answers 3 active oldest votes up vote 7 down vote accepted The standard deviation is a measurement of the "spread" of your data. The analogy I like to use is target shooting. If you're an accurate shooter, your shots cluster very tightly around the bullseye (small standard deviation). If you're not accurate, they are more spread out (la

using Windows 95, 98 or NT. When asked if you want to install the sampling control, click on Yes. When we draw a sample from a population, and calculate a sample statistic such as the mean, http://academic.udayton.edu/gregelvers/psy216/activex/sampling.htm we could ask how well does the sample statistic (called a point estimate) represent the same value for the population? That is, if we calculate the mean of a sample, how close will it be to the mean of the population? Of course, the answer will change depending on the particular sample that we draw. But could we develop a measure that would at least give us an standard error indication of how well we expect the sample mean to represent the population mean? We could subtract the sample mean from the population mean to get an idea of how close the sample mean is to the population mean. (Technically, we don't know the value of the population mean -- if we knew the population mean, then there would be no sense in calculating the sample mean. But in how to reduce theory, it is possible to get an arbitrarily good estimate of the population mean and we can use that estimate as the population mean.) That is, we can calculate how much the sample mean deviates from the population mean. But is this particular sample representative of all of the samples that we could select? It may or may not be. So, we should draw another sample and determine how much it deviates from the population mean. In fact, we might want to do this many, many times. We could then calculate the mean of the deviates, to get an average measure of how much the sample means differ from the population mean. The standard error of the mean does basically that. To determine the standard error of the mean, many samples are selected from the population. For each sample, the mean of that sample is calculated. The standard deviation of those means is then calculated. (Remember that the standard deviation is a measure of how much the data deviate from the mean on average.) The standard deviation of the sample means is defined as the standard error of the mean. It is a measure of how well the point estimate (e.g. the sample mean) re