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

Using wrapr For A Consistent Pipe With ggplot2

John Mount shows how you can use the wrapr pipe to perform data processing and building a ggplot2 visual: Now we can run a single pipeline that combines data processing steps and ggplot plot construction. data.frame(x = 1:20) %.>% mutate(., y = cos(3*x)) %.>% ggplot(., aes(x = x, y = y)) %.>% geom_point() %.>% geom_line() %.>% ggtitle("piped ggplot2") Check […]

Read More

Using R To Hit Azure ML From Power BI

Leila Etaati shows how you can use R to hit an Azure ML endpoint to populate a data set in Power BI: You need to create a model in Azure ML Studio and create a web service for it. The traditional example in Predict a passenger on Titanic ship is going to survived or not? […]

Read More

Categories

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