In this video/ movie clip, I would like to explain the concept of sampling, sampling statistics and confidence interval. Transcript is shown below.

Sampling error is something confusing many people with the concept of population standard deviation (s). Though they related, they are not the same. Assume there is a population (1 million “individuals”) with Gaussian distribution. It has a mean (m) of 10, and standard deviation (s) of 5. What does it mean? You will expect the “individual” having different values and most of them have the value of 10. So, you can draw a graph like this, where the mean and standard deviation is shown. Now, assume you know nothing about the population, and you want to know the mean of the population. What you can do is to pick up 100 individuals randomly from the population and then calculate the mean from the 100 individuals. This is the so-called sampling process with n = 100. But the mean you calculated from the sample (with 100 individuals) probably is not 100. And, if you repeat the sampling process for many times, you will get many different means. But the theory tells us that the mean of these “mean” will be the mean of the population, i.e. 100. So, you can see we have a Gaussian distribution of the sampling mean and the standard deviation (s) of this distribution is called the sampling error. How’s it related to the population standard deviation? It is just:

s = s/sqrt(n).

Ok, so how do I know if the sample mean is far away from the true mean? Answer is you never know! But you can increase you confident on that. This is measured by the confidence interval. For example, we know that in a Gaussian distribution, 95% of the data point lies within 2 standard deviations about the mean. So, if we sample 100 data points, we can confidently say that the mean of the population is within 9.5 to 10.5 at 95% confident level. Here 100%-95% = 5% (a) is called the level of significant and 95% (1-a) is the degree of confidence.