The square root law

Learn the square root law with the app Sampling Distribution

Before the students start with the square root law students should first feel that the SD of the mean becomes smaller as the sample size increases.

From my own class experience I learned that this is a surprising result for many students. I think this intuition must be established before their minds are ready for the root n-law.

The approach I’ve often used

1) Show how the sampling distribution of the mean of a sample of six with the normal distribution is created with the app.

2) Change the sample size to n = 100. Do exactly one sample to make clear what the a sample of 100 means.

3) Ask the question if the SD of the sampling distribution get smaller, larger or stays the same.

4) Allow the computer to simulate.

5) Let the students formulate their reaction on the the result. Let the students try to formulate their explanation of the result.

The self-discovering of the square root n-law is too difficult for a lot of students. What how ever can be done, is that students check the square root law in different situations.
The last four distributions may be tailored with the mouse. Asks the students to make their own distribution with a sigma of 10. Then check the square root in this situation.

From the website www.vustat.eu/teaching/root_law.docx you can download a lesson which follows this path and do much more about the normal approximation to the sampling distribution.