Standard Error (statistics)

1.96)
Lower 95% Limit=x-(y---1.96).

In particular, the standard error of a Sample Statistic (such as Sample Mean ) is the estimated standard deviation of the error in the Process by which it was generated. In other words, it is the standard deviation of the Sampling Distribution of the sample statistic. The notation for standard error can be any one of

SE

SEM

(for standard error of ''measurement'' or ''mean''), or

S_E

.

Standard errors provide simple measures of uncertainty in a value and are often used because:

If the standard error of several individual quantities is known then the standard error of some Function of the quantities can be easily calculated in many cases;

Where the Probability Distribution of the value is known, it can be used to calculate an exact Confidence Interval ; and

Where the probability distribution is unknown, relationships like Chebyshev ’s or the Vysochanskiï-Petunin Inequality can be used to calculate a conservative confidence interval

As the Sample Size tends to infinity the Central Limit Theorem guarantees that the sampling distribution of the mean is asymptotically Normal .

STANDARD ERROR OF THE MEAN

The standard error of the mean of a sample from a Population is
the Standard Deviation of the Sampling Distribution of the mean, and may be estimated by the formula:

:

S_E = rac{\widehat\sigma}{\sqrt{n}}

where

:

\widehat\sigma

is an estimate of the standard deviation σ of the population, and

n

Note: Standard error may also be defined as the standard deviation of the residual error term. (Kenney and Keeping, p. 187; Zwillinger 1995, p. 626)

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Standard Error (statistics)