Standard Error

A standard error of some statistic is the standard deviation of that statistic's sampling distribution.

This concept is particularly common for describing the variance of a sample mean; standard error of the mean is sometimes abbreviated SEM.

Contents

  1. Standard Error
    1. Evaluation
      1. Bernoulli

Evaluation

For an independent sample, the standard error of a mean measurement is the standard deviation of the measurements divided by the root of the sample size: σX‾ = σX/(√n).

Given a random sample of n observations (xi) from a larger unknown population (X), the standard error can be estimated using the sample standard deviation (sX).

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Bernoulli

For a Bernoulli-distributed mean (i.e., p), the true standard error is p(1-p).

When the mean is unknown or abstracted out, it can be appropriate to assume p=0.5. This maximizes the standard error at 0.25, and is generally considered 'close enough' for a mean between 0.2 and 0.8. As an example, when evaluating sampling plans, standard errors can be 'calculated' for subpopulations without considering any specific measurement by assuming the maximum possible error.

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