+ Reply to Thread
Page 1 of 2 1 2 LastLast
Results 1 to 15 of 16

Thread: Computing Power

  1. #1
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Computing Power




    I know that power is one minus beta...but how do you calculate beta?

  2. #2
    Admin
    Points: 20,637, Level: 90
    Level completed: 58%, Points required for next Level: 213
    quark's Avatar
    Location
    Canada
    Posts
    479
    Thanks
    25
    Thanked 196 Times in 73 Posts
    Hi amanning,

    Beta is the type II error. It's the probability of not rejecting H0 when H0 is false.

    To calculate beta, first you need to get the rejection/acceptance region based on your H0, H1 and significance level, then you can get the conditional probability of the acceptance region given H0 is false.

    Let me know if you have further questions.

  3. #3
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Ok. The problem I am working on is Let X:N(?, 64)
    n=16
    H1: m=50
    H2: m>50
    alpha= >.05
    Compute Power for m=56
    (m is mew as I don't know how to type in greek)

  4. #4
    Admin
    Points: 20,637, Level: 90
    Level completed: 58%, Points required for next Level: 213
    quark's Avatar
    Location
    Canada
    Posts
    479
    Thanks
    25
    Thanked 196 Times in 73 Posts
    You want to find the critical value first, then the rejection region, ie reject H0 when sample mean xbar is....

  5. #5
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts
    would this make sense:
    -
    X= 59.29
    Z(59.29)=1.645
    Beta=.05
    1-Beta=.95

  6. #6
    Admin
    Points: 20,637, Level: 90
    Level completed: 58%, Points required for next Level: 213
    quark's Avatar
    Location
    Canada
    Posts
    479
    Thanks
    25
    Thanked 196 Times in 73 Posts
    Quote Originally Posted by amanning
    would this make sense:
    -
    X= 59.29
    Z(59.29)=1.645
    Beta=.05
    1-Beta=.95
    It's more complex than that.

    You have alpha=.05, critical value of 1.645 is correct. Calculate the standard error of the mean, then the critical value is the z-value for the boundary of the rejection region. Rejection region should be Xbar>...

  7. #7
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts
    standard error of the mean:
    2
    found by taking the square root of the variance (variance 64) which is 8 and dividing it by the square root of the sample (square root of 16) which is 4.

  8. #8
    Admin
    Points: 20,637, Level: 90
    Level completed: 58%, Points required for next Level: 213
    quark's Avatar
    Location
    Canada
    Posts
    479
    Thanks
    25
    Thanked 196 Times in 73 Posts
    So you would reject H0 if

    (Xbar-mu)/se_Xbar > 1.645
    (Xbar-50)/2 > 1.645
    Xbar >53.29

    Next we get power directly by calculating P(Xbar >53.29 | mu=56)

    P(Xbar >53.29 | mu=56)
    =P[(Xbar-mu)/se_Xbar > (53.29-mu)/se_Xbar | mu=56]
    =P[Z > (53.29-56)/2]
    =...

    You can do the rest.

  9. #9
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts
    OK, I guess a better question would be how do I figure out the z score?
    I have a 'formula' written down that looks like Z(x)= x-mx/standard error, I don't know what to do with it.

  10. #10
    Admin
    Points: 20,637, Level: 90
    Level completed: 58%, Points required for next Level: 213
    quark's Avatar
    Location
    Canada
    Posts
    479
    Thanks
    25
    Thanked 196 Times in 73 Posts
    Substitute the values.

    P(Xbar >53.29 | mu=56)
    =P[(Xbar-mu)/se_Xbar > (53.29-mu)/se_Xbar | mu=56]
    =P[Z > (53.29-56)/2]
    =P(Z > -1.36)
    =P(Z<1.36)
    =...

    The final answer can be found in the normal table.

  11. #11
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Thank you so much for all of your help. Sometimes I need to see things written differently for them to make sense...

  12. #12
    Admin
    Points: 20,637, Level: 90
    Level completed: 58%, Points required for next Level: 213
    quark's Avatar
    Location
    Canada
    Posts
    479
    Thanks
    25
    Thanked 196 Times in 73 Posts
    You are welcome. Please pass a good word for us. Thanks.

  13. #13
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts
    In reviewing this I do have one more, most likely annoying question, why in post 8 is it x bar -50/2>1.645 and not x bar-56/2>1.645

  14. #14
    Admin
    Points: 20,637, Level: 90
    Level completed: 58%, Points required for next Level: 213
    quark's Avatar
    Location
    Canada
    Posts
    479
    Thanks
    25
    Thanked 196 Times in 73 Posts
    Very good question. When you try to find the rejection region, you use the mu in your H0. After you get the region, you use mu=56, notice I've always included the condition mu=56 afterwards. This is a KEY concept in power calculation.

  15. #15
    Points: 5,237, Level: 46
    Level completed: 44%, Points required for next Level: 113

    Posts
    15
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Smile


    Oooh. I hadn't noticed, or at least hadn't understood. But that makes sense.
    Thanks again...
    I'm sure I'll be back...
    Last edited by amanning; 10-12-2005 at 11:18 PM.

+ Reply to Thread
Page 1 of 2 1 2 LastLast

           




Similar Threads

  1. High power, bias or low power, unbiased?
    By giordano in forum Biostatistics
    Replies: 5
    Last Post: 08-08-2010, 11:53 AM
  2. G*Power Apriori Power Calculation
    By fraenzchen1 in forum Biostatistics
    Replies: 0
    Last Post: 02-16-2010, 06:04 PM
  3. Power calculation vs Power of the study
    By Nice2U in forum Psychology Statistics
    Replies: 5
    Last Post: 10-27-2008, 08:28 AM
  4. Help me out: Computing SE CV SED LSD
    By analyst in forum Statistics
    Replies: 0
    Last Post: 09-13-2006, 08:19 AM
  5. Computing Z-Scores #2
    By sophieb in forum General Discussion
    Replies: 2
    Last Post: 02-26-2006, 08:30 PM

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