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Math Help - What the heck is the standard error?

  1. #1
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    What the heck is the standard error?

    I want to understand better what a standard error really is (I read conflicting things). Can anyone help me to get it?

    Is it correct to say a standard error is the standard deviation of the sampling distribution of a statistic? By sampling distribution I mean a statistic (a mean or a regression coefficient for example) is computed based on a sample and is thus a random variable. That random variable has a distribution. That distribution is called the sampling distribution. The standard deviation of that distribution is the standard error. Am I correct??


    Is a standard error always used as a component in a confidence interval?

    If you are using statistical software and get a "standard error" listed with the point estimate for a regression coefficient lets say, can you multiply it by 1.96 and construct a confidence interval or does it depend on if there are better formulas for the CI?
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  2. #2
    MHF Contributor matheagle's Avatar
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    1.96 is a N(0,1) percentile that gives you 95 precent coverage in your intervals, i.e.,
    P(-1.96<Z<1.96)=.95. So, that's for a two-sided interval with probability .95.

    Now the standard error is the estimate of the standard deviation.
    For example, the variance of the sample mean, for i.i.d. rvs is... V(\bar X)={\sigma^2\over n}.
    Hence the standard deviation of \bar X is {\sigma\over \sqrt n}.
    BUT we usually don't know \sigma, so we estimate the st deviation with this standard error.
    Our estimate of \sigma is S so the standard error of \bar X is {S\over \sqrt n} our standard error.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by B_Miner View Post
    I want to understand better what a standard error really is (I read conflicting things). Can anyone help me to get it?

    Is it correct to say a standard error is the standard deviation of the sampling distribution of a statistic? By sampling distribution I mean a statistic (a mean or a regression coefficient for example) is computed based on a sample and is thus a random variable. That random variable has a distribution. That distribution is called the sampling distribution. The standard deviation of that distribution is the standard error. Am I correct??


    Is a standard error always used as a component in a confidence interval?

    If you are using statistical software and get a "standard error" listed with the point estimate for a regression coefficient lets say, can you multiply it by 1.96 and construct a confidence interval or does it depend on if there are better formulas for the CI?
    See the Wikipedia page

    (note there appear to be two definitions floating about, in one the SE is the standard deviation of the sampling distribution of the statistic in question, and in the other it is the estimate of the SD based on the sample)

    CB
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