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

Bayes’ Theorem In A Picture

Stephanie Glen gives us the basics of Bayes’ Theorem in a picture: Bayes’ Theorem is a way to calculate conditional probability. The formula is very simple to calculate, but it can be challenging to fit the right pieces into the puzzle. The first challenge comes from defining your event (A) and test (B); The second […]

Read More

Tidying Video Game Data

Arvid Kingl has a fun article analyzing data from an open-source video game and applying tidy data principles to it: You will learn what key principles a tidy data set adheres to, why it is useful to follow them consequently, and how to clean the data you are given. Tidying is also a great way […]

Read More

Categories

March 2018
MTWTFSS
« Feb Apr »
 1234
567891011
12131415161718
19202122232425
262728293031