Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

Questions tagged [bessels-correction]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
24 views

Why are the MLE and MMSE corrections for sample variances different?

I have a number of samples of sample size 2 and a number of sample of sample size 3. If my samples are all samples from populations with a shared population variances, I wish to estimate population ...
0
votes
0answers
42 views

Difficulty with averaging corrected sample variances of different degrees of freedom:

I have a number of measurement samples of which some have 2 measurements and some have 3. I wish to make the most accurate estimation of population variance I can, and understand that ignoring data ...
0
votes
1answer
11 views

When to use Bessel correction and and does it alter the standard error?

is there any condition about when to use the Bessel correction as Python uses it to find the Standard Deviation by default. The standard error of the mean is $\...
0
votes
1answer
40 views

How can we write the sample variance's formal definition of a continuous random variable considering Bessel's correction? [closed]

I am trying to find the formal way of writing the sample variance of a continuous random variable considering Bessel's correction. I ask because the sample variance is usually written this way: $$ ...
2
votes
0answers
20 views

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}...
4
votes
1answer
87 views

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 ...
0
votes
1answer
479 views

formula for sample covariance: Bessel's correction

Two options for the sample covariance between X and Y: 1)(with Bessel's) COV(X,Y) = $1/(n-1)$ * $\Sigma$ $(Xi - mean(X))$*$(Yi - mean(Y))$ 2)(without) COV(X,Y) = $1/n$ * $\Sigma$ $(Xi - mean(X))$*$(...
1
vote
0answers
62 views

What is the story of “$n-1$” in the denominator of an estimated variance? [duplicate]

In the book "Numerical Recipes in C" there is said that there is a long story about why the denominator of variance is $N-1$ instead of $N$. If you have never heard that story, you may consult any ...
0
votes
0answers
115 views

Which are the expressions for the variance and standard deviation of a sample?

I have checked several offline and online resources, and they are conflictive. Some define the sample variance as $$s_n^2 = \frac{\sum_{i}^{n}(x_i-\overline{x})^2}{n}$$ That is just the second ...
1
vote
1answer
162 views

Bessel's correction demonstration

I am currently trying to understand the proof of the Bessel's correction Proof of correctness 2 and there is one step in the demonstration that I do not understand: $$ \operatorname{Var}(\bar x) = \...
7
votes
1answer
8k views

Why do we divide by $n-1$ when calculating sample correlation?

I understand the rationale for dividing by $n-1$ when calculating the sample variance, i.e. that if we divide by $n$ we will have an estimate of population variance that is biased to be too low. ...
1
vote
0answers
548 views

Estimation of variance: How to bring Bessel's correction together with degrees of freedom?

I have been considering multiple textbooks to find out the reason that the denominator of the estimation of the population variance is n-1 rather than n. Depending on the book, two reasons are given: ...
3
votes
1answer
209 views

Don't understand the proof that unbiased sample variance is unbiased

Wikipedia gives the following proof why to use Bessel's correction for the unbiased sample variance: \begin{align} E[\sigma_y^2] & = E\left[ \frac 1n \sum_{i=1}^n \left(y_i - \frac 1n \sum_{j=1}^...
8
votes
2answers
10k views

Why is binomial variance calculated as $p(1-p) / (n -1)$?

I had to translate several given statistics equations into code, and I came across this formula: Variance of a simple random sample $= \frac{p(1-p)}{n-1}$ The sample in question are test letters ...
5
votes
2answers
427 views

Could Bessel's correction make sample variance estimation even more biased?

It is well known that Bessel's correction creates an unbiased estimator of variance. What it basically does is divide by $n-1$ instead of $n$. Now what I did is that I chose a few number, like $1,2,3,...
141
votes
15answers
116k views

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 ...