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.

 

[blue_raver22]

I can understand your confusion about how Excel is able to anticipate a sampling distribution using just one sample. However, the answer lies in the fact that Excel uses statistical formulas and algorithms to estimate the sampling distribution based on the characteristics of the single sample provided. These formulas take into account the sample size, the variability of the data, and other statistical parameters to estimate the standard deviation of the sampling distribution and calculate the standard error. This is known as the Central Limit Theorem, which states that regardless of the population distribution, as the sample size increases, the sampling distribution will approach a normal distribution. Therefore, even with just one sample, Excel is able to anticipate a sampling distribution and provide an estimate of the standard error. It is important to note that this is an estimation and may not perfectly reflect the true sampling distribution, but it is a useful tool for statistical analysis and decision making. I hope this helps to clarify your doubts.