Power analysis for comparison of variances of paired samples

[PAULY Vanessa]

Dear list,
Does anyone know if is it possible to calculate the power of a test of comparison of variances for paired data, and how doing this..
Thanks for your help;
Vanessa

[Marta García-Granero]

Hi Vanessa

What do you want to do?:

- Compute the sample size needed to detect a certain variance ratio as
  significant with 80% power.
- Compute the power of a test given a sample size.

PV> Does anyone know if is it possible to calculate the power of
PV> a test of comparison of variances for paired data, and how doing
PV> this..

Anyway, we must start with the formula for comparison of two variances
in paired data:

     (Fratio-1)*SQRT(n-2)
t=-----------------------------
   2*SQRT(Fratio*(1-Rsquare))

Replacing t by Z, and after some math work (rearranging terms), we get
the following:
                  [(Zalfa/2)*SQRT(F0)-Zbeta*SQRT(F1)]^2
n=2+4*(1-Rsquare)---------------------------------------
                          (F1-Fo)^2

Being:

Rsquare: the square of Pearson correlation between pairs
F0: the F ratio under the null hypothesis (usually 1)
F1: the F ratio under the alternate hypothesis (the value worth
    detecting). You must have and idea of its value.
Z(alfa/2): A value related to the desired level of significance (1.96
           for 5%, and 2.578 for 1%)
Zbeta: A value related to the desired power (-0.84 for 80%, -1.28 for
       95%).

As you can see, you can solve for n (given F1, Zalfa and Zbeta) or for
power (given F1, Zalfa and n).


--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Raghda AlAtia]

Hi,

  I unsubscribed few times, but it never worked!  Can somebody please tell me how to unsubscribe?

Thank you.

[Hector Maletta]

The instructions were sent you when you subscribed. You must send a message
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  _____

De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de
Raghda AlAtia
Enviado el: Tuesday, August 01, 2006 10:03 AM
Para: [hidden email]
Asunto: How to unsubscribe



Hi,

  I unsubscribed few times, but it never worked!  Can somebody please tell
me how to unsubscribe?

Thank you.

[Marta García-Granero]

Hi Vanessa

I'd rather be contacted at the list, if you don't mind...

pv> I Want to compute the power of a teste given my sample size,
pv> which is 30 pairs, so I will use your formula.

This can help you:

************* TO COMPUTE SAMPLE SIZE ********************.
MATRIX.
* Manually input data *.
COMPUTE r= 0.578.       /* Correlation between pairs *.
COMPUTE F0= 1.          /* Null hypothesis value *.
COMPUTE F1= 2.          /* Alternate hypothesis *.
COMPUTE Zalfa= 1.95996. /* Replace by  2.57583 if 1% sig. level is wanted *.
COMPUTE Zbeta=-0.84162. /* Replace by -1.28155 if 90% power is wanted *.
* Compute sample size *.
COMPUTE n=2+TRUNC(4*(1-r**2)*((Zalfa*SQRT(F0)-Zbeta*SQRT(F1))**2)/(F1-F0)**2).
PRINT {n+1}
 /FORMAT='F8'
 /TITLE='Minimum sample size needed'.
END MATRIX.


************* TO COMPUTE POWER ********************.
MATRIX.
* Manually input data *.
COMPUTE n=30.           /* Sample size *.
COMPUTE r= 0.578.       /* Correlation between pairs *.
COMPUTE F0=1.           /* Null hypothesis value *.
COMPUTE F1=2.           /* Ratio worth detecting *.
COMPUTE Zalfa= 1.95996. /* Replace by  2.57583 if 1% sig. level is wanted *.
* Compute power *.
COMPUTE Zbeta=Zalfa*SQRT(F0/F1)-0.5*(F1-F0)*SQRT((n-2)/(F1*(1-r**2))).
COMPUTE power=100*(1-CDFNORM(zbeta)).
PRINT power
 /FORMAT='F8.1'
 /TITLE='Observed power'.
END MATRIX.

Regards,

Marta

[Willy B. Winata]

Hi,
I am asking the same question. Could someone please tell us how to unsubscribe from this forum?

Thanks.
  ----- Original Message -----
  From: Raghda AlAtia
  Newsgroups: bit.listserv.spssx-l
  To: [hidden email]
  Sent: Tuesday, August 01, 2006 8:02 PM
  Subject: How to unsubscribe


  Hi,

    I unsubscribed few times, but it never worked!  Can somebody please tell me how to unsubscribe?

  Thank you.

[benard nyakundi]

Hi,

  Was reading some document and came across this analysis that i cud not interpret:

  ... eg 30 people(34%, 95%CI, 1.22% - 6.72%, deff =2.321).

   my dilemma then is how to work out the deff and the range(1.22% - 6.72%)

  Regards

  benard




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[Hector Maletta]

Willy,
It is curious how questions come back again and again. This one has been
explained to you in the welcome message you received when you subscribed,
and it has also been explained many times on this list.
Write a message to [hidden email], and put the following in the
body of the message:
UNSUBSCRIBE SPSSX-L Willy B. Winata
You may replace the word UNSUBSCRIBE with the word SIGNOFF, at your
pleasure.

Hector

-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Willy
B. Winata
Enviado el: Wednesday, August 02, 2006 6:36 AM
Para: [hidden email]
Asunto: Re: How to unsubscribe

Hi,
I am asking the same question. Could someone please tell us how to
unsubscribe from this forum?

Thanks.
  ----- Original Message -----
  From: Raghda AlAtia
  Newsgroups: bit.listserv.spssx-l
  To: [hidden email]
  Sent: Tuesday, August 01, 2006 8:02 PM
  Subject: How to unsubscribe


  Hi,

    I unsubscribed few times, but it never worked!  Can somebody please tell
me how to unsubscribe?

  Thank you.

[lts1]

Hi Bernard,

    The data in this example must be divided into some sort of grouping.  Deff is the design effect.  It gives more insight into the power of ICC.  It can be used to approximate the effective sample size of a model.  It's equal to

        = 1 + (B - 1)(ICC), where B = avg cluster size

     If you divide your N by Deff, you get the effective sample size -- how much you can reduce your sample size & still have effectively the same results.

     I hope this helps.

        Best,
            Lisa

Lisa T. Stickney
Ph.D. Candidate
The Fox School of Business
     and Management
Temple University
[hidden email]



----- Original Message -----
From: "benard nyakundi" <[hidden email]>
Newsgroups: bit.listserv.spssx-l
To: <[hidden email]>
Sent: Wednesday, August 02, 2006 6:04 AM
Subject: Intrepretation of deff

> Hi,
>
>  Was reading some document and came across this analysis that i cud not interpret:
>
>  ... eg 30 people(34%, 95%CI, 1.22% - 6.72%, deff =2.321).
>
>   my dilemma then is how to work out the deff and the range(1.22% - 6.72%)
>
>  Regards
>
>  benard
>
>
>
>
> ---------------------------------
> How low will we go? Check out Yahoo! Messenger's low  PC-to-Phone call rates.
>
>

[Marta García-Granero]

Hi Martin

To the list.... write to the list, please :)

MS> Hi Marta:  I would appreciate it if you could identify what
MS> F0 = 1 represents.  Wouldn't the Null value be .00.

No. Since it is a variance RATIO we are testing, the null value is 1,
not 0.

MS>  Also what does F1=2 represents?

Just an example. You might be interested in detecting lack of HOV only
if the ratio is over 2 (could have been any other value the researcher
is interested in; this was, as I mentioned, just an example).

MS>  If  I understand the syntax for computing sample size you start
MS> out with an observed correlation of .578

Again, just an example. This value should be replaced by the estimated
correlation you might expect between pairs (in post-hoc power
analysis, this value will usually be the observed correlation).

MS> and you want to determine the sample size if power =80%. Is that
MS> correct.

Yes.

MS>  For the program to compute power you start out with a
MS> sample of 20,

30, as a matter of fact. This value is the sample size the study
actually had (that's the value Vanessa told me she had, and I used it
in my example)

MS> a sample correlation of .578, an alpha of .05 and you want to
MS> determine the power.  Is that correct?

Yes

MS> Thanks for you help.

You're wellcome... but I'd rather give help here, not privately.

MS> This can help you:

MS> ************* TO COMPUTE SAMPLE SIZE ********************.
MS> MATRIX.
MS> * Manually input data *.
MS> COMPUTE r= 0.578.       /* Correlation between pairs *.
MS> COMPUTE F0= 1.          /* Null hypothesis value *.
MS> COMPUTE F1= 2.          /* Alternate hypothesis *.
MS> COMPUTE Zalfa= 1.95996. /* Replace by  2.57583 if 1% sig. level is wanted *.
MS> COMPUTE Zbeta=-0.84162. /* Replace by -1.28155 if 90% power is wanted *.
MS> * Compute sample size *.
MS> COMPUTE
MS> n=2+TRUNC(4*(1-r**2)*((Zalfa*SQRT(F0)-Zbeta*SQRT(F1))**2)/(F1-F0)**2).
MS> PRINT {n+1}
MS>  /FORMAT='F8'
MS>  /TITLE='Minimum sample size needed'.
MS> END MATRIX.


MS> ************* TO COMPUTE POWER ********************.
MS> MATRIX.
MS> * Manually input data *.
MS> COMPUTE n=30.           /* Sample size *.
MS> COMPUTE r= 0.578.       /* Correlation between pairs *.
MS> COMPUTE F0=1.           /* Null hypothesis value *.
MS> COMPUTE F1=2.           /* Ratio worth detecting *.
MS> COMPUTE Zalfa= 1.95996. /* Replace by  2.57583 if 1% sig. level is wanted *.
MS> * Compute power *.
MS> COMPUTE
MS> Zbeta=Zalfa*SQRT(F0/F1)-0.5*(F1-F0)*SQRT((n-2)/(F1*(1-r**2))).
MS> COMPUTE power=100*(1-CDFNORM(zbeta)).
MS> PRINT power
MS>  /FORMAT='F8.1'
MS>  /TITLE='Observed power'.
MS> END MATRIX.


--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[msherman]

Pardom my ignorance but why are you bringing in a variance ratio (F=1 and F=2) when testing for a correlation.
The correlation is the covariance divided by the square root (vaxX*VarY). What am I missing.

>>> Marta García-Granero             <[hidden email]> 08/02/06 1:33 PM >>>
Hi Martin

To the list.... write to the list, please :)

MS> Hi Marta:  I would appreciate it if you could identify what
MS> F0 = 1 represents.  Wouldn't the Null value be .00.

No. Since it is a variance RATIO we are testing, the null value is 1,
not 0.

MS>  Also what does F1=2 represents?

Just an example. You might be interested in detecting lack of HOV only
if the ratio is over 2 (could have been any other value the researcher
is interested in; this was, as I mentioned, just an example).

MS>  If  I understand the syntax for computing sample size you start
MS> out with an observed correlation of .578

Again, just an example. This value should be replaced by the estimated
correlation you might expect between pairs (in post-hoc power
analysis, this value will usually be the observed correlation).

MS> and you want to determine the sample size if power =80%. Is that
MS> correct.

Yes.

MS>  For the program to compute power you start out with a
MS> sample of 20,

30, as a matter of fact. This value is the sample size the study
actually had (that's the value Vanessa told me she had, and I used it
in my example)

MS> a sample correlation of .578, an alpha of .05 and you want to
MS> determine the power.  Is that correct?

Yes

MS> Thanks for you help.

You're wellcome... but I'd rather give help here, not privately.

MS> This can help you:

MS> ************* TO COMPUTE SAMPLE SIZE ********************.
MS> MATRIX.
MS> * Manually input data *.
MS> COMPUTE r= 0.578.       /* Correlation between pairs *.
MS> COMPUTE F0= 1.          /* Null hypothesis value *.
MS> COMPUTE F1= 2.          /* Alternate hypothesis *.
MS> COMPUTE Zalfa= 1.95996. /* Replace by  2.57583 if 1% sig. level is wanted *.
MS> COMPUTE Zbeta=-0.84162. /* Replace by -1.28155 if 90% power is wanted *.
MS> * Compute sample size *.
MS> COMPUTE
MS> n=2+TRUNC(4*(1-r**2)*((Zalfa*SQRT(F0)-Zbeta*SQRT(F1))**2)/(F1-F0)**2).
MS> PRINT {n+1}
MS>  /FORMAT='F8'
MS>  /TITLE='Minimum sample size needed'.
MS> END MATRIX.


MS> ************* TO COMPUTE POWER ********************.
MS> MATRIX.
MS> * Manually input data *.
MS> COMPUTE n=30.           /* Sample size *.
MS> COMPUTE r= 0.578.       /* Correlation between pairs *.
MS> COMPUTE F0=1.           /* Null hypothesis value *.
MS> COMPUTE F1=2.           /* Ratio worth detecting *.
MS> COMPUTE Zalfa= 1.95996. /* Replace by  2.57583 if 1% sig. level is wanted *.
MS> * Compute power *.
MS> COMPUTE
MS> Zbeta=Zalfa*SQRT(F0/F1)-0.5*(F1-F0)*SQRT((n-2)/(F1*(1-r**2))).
MS> COMPUTE power=100*(1-CDFNORM(zbeta)).
MS> PRINT power
MS>  /FORMAT='F8.1'
MS>  /TITLE='Observed power'.
MS> END MATRIX.


--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Marta García-Granero]

Hi Martin


MS> Pardom my ignorance but why are you bringing in a variance
MS> ratio (F=1 and F=2) when testing for a correlation.
MS> The correlation is the covariance divided by the square root
MS> (vaxX*VarY). What am I missing.

Perhaps Vanessa's original question?: "Power analysis for COMPARISON OF
VARIANCES OF PAIRED SAMPLES". I'm not doing power analysis for a
correlation coefficient, but for a variance ratio (biggest
variance/smallest variance) in paired samples. Since the formula for
testing a variance ratio (a t test) includes the correlation between
pairs of measures, the formula derived from it that is used for power
analysis also needs an estimate of that correlation:

    (Fratio-1)*SQRT(n-2)
t=------------------------
  SQRT(Fratio*(1-Rsquare))

Hence, the null value for F under H0 is 1 instead of 0.



--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[chu082011]

Hi,

Thanks for sharing. Any way, your points of view make me thinking about some thing for my project.

Get your ideas first! You can see suggestions at source:  Paired comparison analysis

Tks and best regards