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Related Concept Videos

Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

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The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
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Standard Error of the Mean01:13

Standard Error of the Mean

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The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.The standard error of the mean is an example of a standard error. It is a unique standard deviation known as the standard deviation of the sampling distribution of the mean. The standard error of the mean is a statistic that calculates how correctly a sample distribution represents a...
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Calculating Standard Deviation01:08

Calculating Standard Deviation

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The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. Further, the standard deviation is always a positive value or zero.
The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Computation of standard errors.

Bryan E Dowd, William H Greene, Edward C Norton

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    |May 7, 2014
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    Summary
    This summary is machine-generated.

    This study presents methods for calculating standard errors of functions with estimated parameters. It offers computer code for the delta method, Krinsky-Robb, and bootstrapping in Stata and LIMDEP.

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    Area of Science:

    • Econometrics
    • Statistical Computing

    Background:

    • Estimating standard errors for functions of model parameters is crucial for accurate statistical inference.
    • Existing methods may not fully account for all sources of variation, particularly in complex models.

    Purpose of the Study:

    • To provide and compare computational methods for standard errors of functions involving estimated parameters.
    • To offer practical computer code for implementing these methods.

    Main Methods:

    • The study demonstrates the calculation of standard errors for predicted values and variable effects.
    • Three computational approaches are detailed: the delta method, Krinsky-Robb, and bootstrapping.
    • Computer code is provided for Stata 12 and LIMDEP 10/NLOGIT 5.

    Main Results:

    • The delta method, Krinsky-Robb, and bootstrapping are presented as viable options for computing standard errors.
    • The choice of method often depends on computational convenience for most applications.
    • Specific considerations arise when calculating standard errors for sample averages of functions involving parameters and nonstochastic variables.

    Conclusions:

    • The selection of a standard error computation method is generally flexible.
    • Careful consideration of variation sources is essential when computing standard errors for sample averages of functions with estimated parameters and nonstochastic variables.