a sampling distribution

That’s probably the distribution in the sample. Which you hope matches the distribution of the population. Right?

through repeatedly drawing samples of the same size from a population.

So yes, but this *repeatedly* might be important.

One of the useful functions of sampling distributions is to characterize how sample statistics relate to population parameters.

Say more..

sampling distributions are distributions of values of a statistic instead of distributions of individual scores

This seems very important as well. Scores again. I’d like to have some concrete examples soon, I may be closer than I think.

the expected value of the sample means of these samples will equal the population mean

Great.

Recall Y bar is the sample mean.

And the above is kind of what we expect. Maybe you have to have a normal distribution? Ah..

where every score has an equal chance of inclusion

That’s not normal. That’s something else. Equal chance. Equal as many As as Bs as Cs as Fs. Equal as many Shaqs as Dr. Evils. Probably a better token short guy.

I think I have questions around ‘population parameters’. What is that again? Like a mean, median, mode, a stat about the population?

Recall

greek letters for population parameters.

So mean for mu so yeah. Why aren’t greek characters in my emoji picker? 😘 = while the first result for mu, not the same as the mean.

This also serves to define one of the desirable properties of statistics. That is, a sample statistic is said to be an unbiased estimator of a population parameter when the expected value of the statistic (or, equivalently, the mean of the sampling distribution of the statistic) equals the value of the parameter

Meditate on these things.

I’m very glad there’s a lab portion to this class since I think most of this material is like terrain that needs to be traversed, corners to be checked behind.

But, the distinction of sample and population is not to be confused. The data you collect is not the population. Hopefully it is representative, but not the same.

## Leave a Reply