+ Reply to Thread
Results 1 to 7 of 7

Thread: difference between estimating variance and standard deviation.

  1. #1
    Points: 689, Level: 13
    Level completed: 78%, Points required for next Level: 11

    Posts
    11
    Thanks
    3
    Thanked 0 Times in 0 Posts

    difference between estimating variance and standard deviation.




    In a simulation study, is there any difference between

    \bullet to estimate the variance \sigma^2, 1000 times and taking its average,
    and

    \bullet to estimate the standard deviation \sigma, 1000 times and taking its average?

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

  2. #2
    Omega Contributor
    Points: 38,334, Level: 100
    Level completed: 0%, Points required for next Level: 0
    hlsmith's Avatar
    Location
    Not Ames, IA
    Posts
    6,998
    Thanks
    398
    Thanked 1,186 Times in 1,147 Posts

    Re: difference between estimating variance and standard deviation.

    What is your purpose or goal?
    Stop cowardice, ban guns!

  3. #3
    Devorador de queso
    Points: 95,819, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,935
    Thanks
    307
    Thanked 2,629 Times in 2,245 Posts

    Re: difference between estimating variance and standard deviation.

    Quote Originally Posted by hlsmith View Post
    What is your purpose or goal?
    I don't have emotions and sometimes that makes me very sad.

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

    spunky (02-19-2017)

  5. #4
    TS Contributor
    Points: 22,411, Level: 93
    Level completed: 7%, Points required for next Level: 939
    spunky's Avatar
    Location
    vancouver, canada
    Posts
    2,135
    Thanks
    166
    Thanked 537 Times in 431 Posts

    Re: difference between estimating variance and standard deviation.

    Quote Originally Posted by dason View Post
    omg! Good stuff rite there!
    for all your psychometric needs! https://psychometroscar.wordpress.com/about/

  6. #5
    Super Moderator
    Points: 13,151, Level: 74
    Level completed: 76%, Points required for next Level: 99
    Dragan's Avatar
    Location
    Illinois, US
    Posts
    2,014
    Thanks
    0
    Thanked 223 Times in 192 Posts

    Re: difference between estimating variance and standard deviation.

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

    \bullet to estimate the variance \sigma^2, 1000 times and taking its average,
    and

    \bullet to estimate the standard deviation \sigma, 1000 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. #6
    Human
    Points: 12,676, Level: 73
    Level completed: 57%, Points required for next Level: 174
    Awards:
    Master Tagger
    GretaGarbo's Avatar
    Posts
    1,362
    Thanks
    455
    Thanked 462 Times in 402 Posts

    Re: difference between estimating variance and standard deviation.

    Quote Originally Posted by hlsmith View Post
    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. #7
    Super Moderator
    Points: 13,151, Level: 74
    Level completed: 76%, Points required for next Level: 99
    Dragan's Avatar
    Location
    Illinois, US
    Posts
    2,014
    Thanks
    0
    Thanked 223 Times in 192 Posts

    Re: difference between estimating variance and standard deviation.


    Quote Originally Posted by GretaGarbo View Post
    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)

+ Reply to Thread

           




Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats