# Questions tagged [bessels-correction]

Bessel's correction lies in dividing by $n-1$ instead of $n$ in computing the sample variance.

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### Efficient proof of Bessel's correction

I am beginning to learn the fundamentals of statistics, and I am reading the proof of why Bessel's correction in the estimate of the variance works from the wikipedia page about it. I understand ...
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### Z-score and standard error in linear regression

I am reading Elements of statistical learning, and in the chapter on linear regression, I cannot understand the following: We have estimated the regression parameters $\beta_1, ..., \beta_p$ from $N$ ...
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### Notation for distributions on subspaces

Question What notation should I use for a normal distribution on a subspace $U \subset \mathbb{R}^n$? Motivation I have a geometric intuition for Bessel's correction which goes something like this: A ...
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### Tail of the CDF of noncentral chi-squared RV

The pdf and cdf of the non-central chi squared RV (under the scenario I am studying) is given as follows: \begin{align} &f(x)=\frac{1}{v} \exp\left(\frac{-(a+x)}{v}\right)I_{0}\left(\frac{\sqrt{xa}...
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### Degrees of Freedom In Sample Variance

Recall the formula for sample variance $$s_{n - 1}^2 = \dfrac{1}{n -1} \sum_{i = 1}^n (\bar{x} - x_i)^2,$$ where $\bar{x}$ is the sample mean. There are many proofs for why $s_{n - 1}^2$ is an ...
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### Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
I was asked today in class why you divide the sum of square error by $n-1$ instead of with $n$, when calculating the standard deviation. I said I am not going to answer it in class (since I didn't ...