Monday, September 12, 2016

Kristoffer Magnusson's "Interpreting Confidence Intervals"

I have shared Kristoffer Magnusson's fantastic visualizations of statistical concepts here previously (correlation, Cohen's d). Here is another one that helps to explain confidence intervals, and how the likelihood of an interval containing true mu varies based on interval size as well as the size of the underlying sample.

The site is interactive in two ways. 1) The sliding bar at the top of the page allows you to adjust the size of the confidence interval, which you can read in the portion of the page labeled "CI coverage %" or directly above the CI ticker. See below.

2) You can also change the n-size for the samples the simulation is pulling.

The site also reports back the number of samples that include mu and the number of samples that miss mu (wee little example for Type I/Type II error).

How to use in class:

Students will see how intervals increase and decrease in size as you reset the CI percentage. As the sample size increases, the range of the intervals decrease and the sample means converge upon true mu. As confidence interval decreases, the range also decreases.

This is useful for teaching good ol' confidence intervals (as a compliment to the mean) but also to teach confidence intervals as they become an increasingly popular alternative to NHST.