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How does Excel anticipate a sampling distribution using just one sample?

  1. Jan 27, 2012 #1
    Hi,

    I know that Standard Error of a coefficient is the standard deviation of the sampling distribution associated with the coefficient. I understand the concept.

    What puzzles me is this: We have just one random sample to work with. The calculator or Excel doesn’t have any info on the actual population or any other sample. Then how can it anticipate a sampling distribution and calculate its standard deviation to give us the Standard Error?

    Thanks.
     
  2. jcsd
  3. Jan 27, 2012 #2
    The standard error of the mean is [itex] SE = s/\sqrt {n} [/itex] where s is the sample standard deviation. In other words you are estimating the population [itex]\sigma[/itex] from the sample of size n. The concept is that a truly random sample can yield a valid estimate of [itex]\sigma[/itex]. Obviously, as an estimate, it can be refined by additional sampling. The Central Limit Theorem states that the estimates of the mean will tend toward a normal distribution regardless of the population distribution. It's clear that the SE declines with increasing n for fixed s.
     
    Last edited: Jan 27, 2012
  4. Jan 27, 2012 #3
    Thanks SW VandeCarr.


    I thought SE is the std dev of the sampling distribution.
     
  5. Jan 27, 2012 #4
    Yes, but that's not the same as the sd of the individual sample. The terminology is a bit confusing. I suggest you look it up.
     
    Last edited: Jan 27, 2012
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