  julian Community Manager

## Simulating the estimation of the population variance (Why n-1?)

Video Demo

The attached script is useful for demonstrating the bias in estimating the population variance/standard deviation without using the corrected sample estimator (with n-1). This script can be used during lecture to demonstrate the concept, or can be given to students to use an an exploratory exercise.

Usage:

1. Run the attached script by pressing Control-R (on the PC), and Command-R (on the Mac).

2. Specify the population parameters, sample size, and number of sample to draw. (10k or more samples is recommended, and should take less than ~3 seconds on most computers) 3. The table of sample estimates will be generated, including:

• Sample Number
• Sample Size
• Sums of Squares for each sample
• Variance, estimated using the population form (with N in the denominator)
• Variance, estimated using the sample estimator form (with n-1 in the denominator)
• Standard Deviation, estimated using the population form (with N in the denominator)
• Standard Deviation, estimated using the sample estimator form (with n-1 in the denominator) 4. Run the saved scripts in the table to visualize and interact with the observed estimates. In the interface you can:

• Show the population variance/standard deviation on the histogram
• Show the observed mean estimate of the selected statistic For ideas on using this script, see the Video Demo that I use in my course.

This script was developed in collaboration with mia.stephens. Please post any suggestions for future versions.

We hope this helps with your teaching!

julian

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