Linked Questions

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1answer
8k views

why sample variance has has n-1 in the denominator? [duplicate]

Sample variance is calculated according to: $s^2=\frac{\sum{(x-\bar{x})^2}}{n-1}$ Population variance is calculated according to: $\sigma^2=\frac{\sum{(x-\mu)^2}}{n}$ Why denominator for sample ...
8
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1answer
141 views

Alternate (?) definition of sample variance [duplicate]

The variance of a sample can be defined as $$s^2 = \frac{1}{2}\frac{1}{n(n-1)}\sum_{i}\sum_{j\ne i}\left(x_i - x_j\right)^2$$ Apart from the factor of $1/2$, this can be paraphrased verbally as ...
1
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1answer
574 views

The derivation of standard deviation [duplicate]

So, if there are $N$ data points in my sample space of any randomly distributed variable $X$. The standard deviation, $\sigma$, (from my understanding) is the root mean squared of the error (from the ...
0
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1answer
221 views

Estimates of variance from an iid sample [duplicate]

There are two kinds of estimates of variance from an iid sample $X1, \dots, X_n$ $1/n * \sum_i (X_i - \bar{X})^2$, which is MLE $1/(n-1) * \sum_i (X_i - \bar{X})^2$, which is unbiased. The unbiased ...
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0answers
133 views

Intuition behind Besel's correction for an unbiased estimate of the variance [duplicate]

We have two estimators for samples dispersion: $\frac{1}{n}\sum_1^n (X_i - \overline{X_n})^2$ and $\frac{1}{n - 1}\sum_1^n (X_i - \overline{X_n})^2$. The second estimator unbiased - it has ...
0
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1answer
66 views

Why Standard deviation formula has n-1 in the denominator but Variance only n? [duplicate]

If is true that SQRT(Variance) = SD then one cannot have n-1 in the denominator and the other not but should be same? SD formula: Variance formula:
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0answers
69 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 ...
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0answers
27 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, ...
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0answers
18 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 ...
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0answers
17 views

Show estimator is unbiased [duplicate]

Consider the estimator of the variance given by the formula: $(S')^2 = \frac{1}{n} \sum_{i=1}^{n}(Y_i − µ)^2$ Is this a biased or unbiased estimator? I'm not sure if it is possible to prove ...
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0answers
14 views

Degree of freedom [duplicate]

Why do we use degree of freedom while dealing with samples(e.g. while calculating t statistic and sample variance, we divide by $ n-1 $ degree of freedom, but while calculating z score and population ...
71
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5answers
38k views

How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?

The formula for computing variance has $(n-1)$ in the denominator: $s^2 = \frac{\sum_{i=1}^N (x_i - \bar{x})^2}{n-1}$ I've always wondered why. However, reading and watching a few good videos about "...
16
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3answers
4k views

Why does one have to use REML (instead of ML) for choosing among nested var-covar models?

Various descriptions on model selection on random effects of Linear Mixed Models instruct to use REML. I know difference between REML and ML at some level, but I don't understand why REML should be ...
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3answers
2k views

When estimating variance, why do unbiased estimators divide by n-1 yet maximum likelihood estimates divide by n?

I am totally confused: On the one hand you can read all kinds of explanations why you have to divide by n-1 to get an unbiased estimator for the (unknown) population variance (degrees of freedom, not ...
3
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1answer
8k views

What is the difference between Mean Squared Deviation and Variance?

I am doing some tutoring for an AS-Level maths student and unfortunately for me they are doing statistics. This is not my strong point, mainly from the point of view of remembering all of the ...

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