Why Does Empirical Variance Use n-1 Instead Of n?

Sebastian Sauer gives us a simulation showing why we use n-1 instead of n as the denominator when calculating the variance of a sample:

Our results show that the variance of the sample is smaller than the empirical variance; however even the empirical variance too is a little too small compared with the population variance (which is 1). Note that sample size was n=10 in each draw of the simulation. With sample size increasing, both should get closer to the “real” (population) sample size (although the bias is negligible for the empirical variance). Let’s check that.

This is an R-heavy post and does a great job of showing that it’s necessary, and ends with  recommended reading if you want to understand the why.

Related Posts

Building an Image Classifier with PyTorch

Rogier van der Geer shows how you can use PyTorch to build out a Convolutional Neural Network for image classification: The tool that we are going to use to make a classifier is called a convolutional neural network, or CNN. You can find a great explanation of what these are right here on wikipedia. But we […]

Read More

xgboost and Small Numbers of Subtrees

John Mount covers an interesting issue you can run into when using xgboost: While reading Dr. Nina Zumel’s excellent note on bias in common ensemble methods, I ran the examples to see the effects she described (and I think it is very important that she is establishing the issue, prior to discussing mitigation).In doing that I ran into one more […]

Read More


March 2018
« Feb Apr »