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

[musicgold]

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.

 

[SW VandeCarr]

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.

The standard error of the mean is $SE = s/\sqrt {n}$ where s is the sample standard deviation. In other words you are estimating the population $\sigma$ from the sample of size n. The concept is that a truly random sample can yield a valid estimate of $\sigma$. 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.

 

[musicgold]

Thanks SW VandeCarr.

In other words you are estimating the population σ from the sample of size n.

I thought SE is the std dev of the sampling distribution.

 

[SW VandeCarr]

Thanks SW VandeCarr.
I thought SE is the std dev of the sampling distribution.

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.