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

1. Jan 27, 2012

### 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.

2. Jan 27, 2012

### SW VandeCarr

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.

Last edited: Jan 27, 2012
3. Jan 27, 2012

### musicgold

Thanks SW VandeCarr.

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

4. Jan 27, 2012

### SW VandeCarr

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