Thread: difference between estimating variance and standard deviation.

1. difference between estimating variance and standard deviation.

In a simulation study, is there any difference between

to estimate the variance , times and taking its average,
and

to estimate the standard deviation , times and taking its average?

Can I do anyone of these? Is there any preference of doing a particular one?

2. Re: difference between estimating variance and standard deviation.

What is your purpose or goal?

3. Re: difference between estimating variance and standard deviation.

Originally Posted by hlsmith
What is your purpose or goal?

4. The Following User Says Thank You to Dason For This Useful Post:

spunky (02-19-2017)

5. Re: difference between estimating variance and standard deviation.

Originally Posted by dason
omg! Good stuff rite there!

6. Re: difference between estimating variance and standard deviation.

Originally Posted by user1234
In a simulation study, is there any difference between

to estimate the variance , times and taking its average,
and

to estimate the standard deviation , times and taking its average?

Can I do anyone of these? Is there any preference of doing a particular one?
Just consider the fact that the variance estimate of the population variance is unbiased, whereas the estimate associated with the standard deviation is not an unbiased estimate of the population standard deviation. There's your answer.

7. The Following User Says Thank You to Dragan For This Useful Post:

user1234 (03-10-2017)

8. Re: difference between estimating variance and standard deviation.

Originally Posted by hlsmith
What is your purpose or goal?
The purpose is to talk about what Hillary and Roger are talking about after about 40 minutes.

https://soundcloud.com/nssd-podcast/...w-times#t=0:00

The sample variance is unbiased but the sample standard deviation in not unbiased and I find that so strange. Also, as they discuss: the bias and variance trade off.

9. Re: difference between estimating variance and standard deviation.

Originally Posted by GretaGarbo
The purpose is to talk about what Hillary and Roger are talking about after about 40 minutes.

The sample variance is unbiased but the sample standard deviation in not unbiased and I find that so strange.
Well, it's really not strange. In short, taking the square root of the variance is a non-linear transformation.

That said, if we assume that the population is normally distributed, then an unbiased estimate of the standard deviation (s) of the population standard deviation (Sigma) is as follows:

E[s] = [ (4*n - 4) / (4n - 3 ] * Sigma.

Thus, we have:

E { [ 1 + 1 / (4*(n - 1)) ] * s } = Sigma

10. The Following User Says Thank You to Dragan For This Useful Post:

GretaGarbo (02-20-2017)

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