standard error

(noun)

A measure of how spread out data values are around the mean, defined as the square root of the variance.

Related Terms

Examples of standard error in the following topics:

  • Standard Error

    • The standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations.
    • This is due to the fact that the standard error of the mean is a biased estimator of the population standard error.
    • The relative standard error (RSE) is simply the standard error divided by the mean and expressed as a percentage.
    • If one survey has a standard error of $10,000 and the other has a standard error of $5,000, then the relative standard errors are 20% and 10% respectively.
    • Paraphrase standard error, standard error of the mean, standard error correction and relative standard error.

  • Which Standard Deviation (SE)?

    • Although they are often used interchangeably, the standard deviation and the standard error are slightly different.
    • The standard error is the standard deviation of the sampling distribution of a statistic.
    • 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.
    • However, the mean and standard deviation are descriptive statistics, whereas the mean and standard error describes bounds on a random sampling process.
    • Standard error should decrease with larger sample sizes, as the estimate of the population mean improves.

  • Estimating the Accuracy of an Average

    • The standard error of the mean is the standard deviation of the sample mean's estimate of a population mean.
    • In general terms, the standard error is the standard deviation of the sampling distribution of a statistic.
    • Note that the standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations because the standard error of the mean is a biased estimator of the population standard error.
    • 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.
    • 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.

  • Examining the standard error formula

    • The formula for the standard error of the difference in two means is similar to the formula for other standard errors.
    • Recall that the standard error of a single mean, $\bar{x}_1$, can be approximated by
    • where s1 and n1 represent the sample standard deviation and sample size.
    • The standard error of the difference of two sample means can be constructed from the standard errors of the separate sample means:
    • 5.14: The standard error squared represents the variance of the estimate.

  • Standard Error of the Estimate

    • Make judgments about the size of the standard error of the estimate from a scatter plot
    • Compute the standard error of the estimate based on errors of prediction
    • Estimate the standard error of the estimate based on a sample
    • In fact, σest is the standard deviation of the errors of prediction (each Y - Y' is an error of prediction).
    • Therefore, the standard error of the estimate is

  • Standard error of the mean

    • The standard deviation associated with an estimate is called the standard error.
    • 4.5: (a) Use Equation (4.4) with the sample standard deviation to compute the standard error: .
    • Our sample is about 1 standard error from
    • Our sample is about 1 standard error from 36 years.
    • (We use the standard error to identify what is close.

  • Expected Value and Standard Error

    • Expected value and standard error can provide useful information about the data recorded in an experiment.
    • The standard error is the standard deviation of the sampling distribution of a statistic.
    • The standard error of the mean (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 of a given size drawn from the population.
    • The standard error of the sum can be calculated by the square root of number of draws multiplied by the standard deviation of the box: $\sqrt{25} \cdot \text{SD of box} = 5\cdot 1.17 = 5.8$.
    • Solve for the standard error of a sum and the expected value of a random variable

  • Properties of Sampling Distributions

    • This standard deviation is called the standard error of the mean.
    • The standard deviation of the sampling distribution of a statistic is referred to as the standard error of that quantity.
    • For the case where the statistic is the sample mean, and samples are uncorrelated, the standard error is:
    • To be specific, assume your sample mean is 125 and you estimated that the standard error of the mean is 5.
    • Describe the general properties of sampling distributions and the use of standard error in analyzing them

  • Chance Error and Bias

    • Chance error and bias are two different forms of error associated with sampling.
    • In statistics, a sampling error is the error caused by observing a sample instead of the whole population.
    • In sampling, there are two main types of error: systematic errors (or biases) and random errors (or chance errors).
    • Random error always exists.
    • These are often expressed in terms of its standard error:

  • Summary of Formulas

    • ( lower value,upper value ) = ( point estimate − error bound,point estimate + error bound )
    • Formula 8.2: To find the error bound when you know the confidence interval
    • error bound = upper value − point estimate OR error bound = (upper value − lower value)/2