# 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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### Why use n-1 in the sample variance when random tests show little differences between a "n-1 standard deviation" and a "n standard deviation"? [duplicate]

I generated random tests to calculate standard deviations of populations and samples using both n-1 and n for the denominator of the variance formula with datasets like [5,20,25... numbers between 5-...
113 views

### Why do we prefer unbiased estimators instead of minimizing MSE?

I was thinking about why, usually, $\hat{\sigma}^2=\hat{p}(1-\hat{p})$ is used to estimate the variance in a Bernoulli population instead of $s^2=\hat{p}(1-\hat{p})\frac{n}{n-1}$. $s^2$ is unbiased, ...
626 views

### Is Bessel's correction required when calculating mean?

Bessel's correction is used for the variance calculation from samples. In my understanding the reason is because the mean of samples has an error or bias from the true mean, and dividing by (n-1) ...
77 views

### Where to find a citation for the n/(n+1) sample variance correction?

In my Master's thesis project I could not show my (normally-distributed) samples to have a common population variance (through Levene's test or otherwise), so I could not use the n/(n-1) Bessel's ...
232 views

### Generalization of Bessel's correction to higher order models? [duplicate]

Multiplying sample variance (i.e. variance from sample mean) by $\frac{n}{n-1}$ to obtain an unbiased estimate of the population variance (i.e. variance from population mean) is called Bessel's ...
30 views

### Is there ever a right time to not use Bessel's Correction? [duplicate]

I can not find a clear explanation for when NOT to use Bessel's correction and use N instead of N-1. As I understand it, Bessel's correction would apply to things such as clinical trials, sampling ...
40 views

### Explanation for Bessel's correction [duplicate]

In textbooks and online the explanation for Bessel's correction is that the sample points are closer to the sample mean than the population mean.This is true for sampling with replacement as well. So, ...
92 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 ...
63 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 ...
### 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 ...