Comparing two Sobel's Z

[NomiW]

Hello all,

I have run 2 mediation models, one for males and one for females. Using
Sobel's mediation test (with very large samples) I found a significant
mediation path for both sexes. I'm interesting in comparing the two, i.e. the
Sobel's Z for females is 13 and for males 21. I'd like to know whether these
are significantly different. Is there a way to do this?

Thanks,

Nomi Werbeloff, PhD

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[Bruce Weaver]

The forumula for Sobel's z is shown on this page:

   http://quantpsy.org/sobel/sobel.htm

The denominator of that expression is the SE for the z-test.  Square it (i.e., remove the SQRT sign) to get a variance.  Add together the two variances (i.e., for males and females) and take the square root of that sum to get the SE of the difference.  Then run another z-test as follows:

z = (a_m*b_m - a_f*b_f) / SE_diff

where the _m and _f indicate for males and females respectively.

The general principle is that the variance of a difference = the sum of the variances (when you have two independent samples).  

HTH.
 

Nomi wrote

Hello all,

I have run 2 mediation models, one for males and one for females. Using
Sobel's mediation test (with very large samples) I found a significant
mediation path for both sexes. I'm interesting in comparing the two, i.e. the
Sobel's Z for females is 13 and for males 21. I'd like to know whether these
are significantly different. Is there a way to do this?

Thanks,

Nomi Werbeloff, PhD

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[Alexander J. Shackman-2]

Sometimes I have done this meta-analytically, by converting Z to an estimate of effect-size (r), and comparing the two correlation coefficients. Off the top of my head, I'm not sure how the two techniques will differ in their sensitivity or control of Type I error.

HTH,

Alex Shackman

On Thu, Sep 6, 2012 at 9:34 AM, Bruce Weaver <[hidden email]> wrote:

The forumula for Sobel's z is shown on this page:

   http://quantpsy.org/sobel/sobel.htm

The denominator of that expression is the SE for the z-test.  Square it
(i.e., remove the SQRT sign) to get a variance.  Add together the two
variances (i.e., for males and females) and take the square root of that sum
to get the SE of the difference.  Then run another z-test as follows:

z = (a_m*b_m - a_f*b_f) / SE_diff

where the _m and _f indicate for males and females respectively.

The general principle is that the variance of a difference = the sum of the
variances (when you have two independent samples).

HTH.



Nomi wrote
>
> Hello all,
>
> I have run 2 mediation models, one for males and one for females. Using
> Sobel's mediation test (with very large samples) I found a significant
> mediation path for both sexes. I'm interesting in comparing the two, i.e.
> the
> Sobel's Z for females is 13 and for males 21. I'd like to know whether
> these
> are significantly different. Is there a way to do this?
>
> Thanks,
>
> Nomi Werbeloff, PhD
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> LISTSERV@.UGA (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>




-----
--
Bruce Weaver
[hidden email]
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"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
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--
Alexander J. Shackman, Ph.D.
HealthEmotions Research Institute | Lane Neuroimaging Laboratory
Wisconsin Psychiatric Institute & Clinics
University of Wisconsin-Madison
6001 Research Park Boulevard
Madison, Wisconsin 53719

Telephone: [phone]
Fax: [phone]
Email: [hidden email]
http://psyphz.psych.wisc.edu/~shackman

[Bruce Weaver]

Hi Alex.  Do you mean that you compare them via the test of heterogeneity (Q) typically used by meta-analysts?  Q is distributed (approximately) as chi-square, so when you compare only two estimates via Q, the square root of Q = z.  But your conversion of z to r might change things.

Alexander J. Shackman-2 wrote

Sometimes I have done this meta-analytically, by converting Z to an
estimate of effect-size (r), and comparing the two correlation
coefficients. Off the top of my head, I'm not sure how the two techniques
will differ in their sensitivity or control of Type I error.

HTH,
Alex Shackman

On Thu, Sep 6, 2012 at 9:34 AM, Bruce Weaver <[hidden email]>wrote:

> The forumula for Sobel's z is shown on this page:
>
>    http://quantpsy.org/sobel/sobel.htm
>
> The denominator of that expression is the SE for the z-test.  Square it
> (i.e., remove the SQRT sign) to get a variance.  Add together the two
> variances (i.e., for males and females) and take the square root of that
> sum
> to get the SE of the difference.  Then run another z-test as follows:
>
> z = (a_m*b_m - a_f*b_f) / SE_diff
>
> where the _m and _f indicate for males and females respectively.
>
> The general principle is that the variance of a difference = the sum of the
> variances (when you have two independent samples).
>
> HTH.
>
>
>
> Nomi wrote
> >
> > Hello all,
> >
> > I have run 2 mediation models, one for males and one for females. Using
> > Sobel's mediation test (with very large samples) I found a significant
> > mediation path for both sexes. I'm interesting in comparing the two, i.e.
> > the
> > Sobel's Z for females is 13 and for males 21. I'd like to know whether
> > these
> > are significantly different. Is there a way to do this?
> >
> > Thanks,
> >
> > Nomi Werbeloff, PhD
> >
> > =====================
> > To manage your subscription to SPSSX-L, send a message to
> > LISTSERV@.UGA (not to SPSSX-L), with no body text except the
> > command. To leave the list, send the command
> > SIGNOFF SPSSX-L
> > For a list of commands to manage subscriptions, send the command
> > INFO REFCARD
> >
>
>
>
>
> -----
> --
> Bruce Weaver
> [hidden email]
> http://sites.google.com/a/lakeheadu.ca/bweaver/
>
> "When all else fails, RTFM."
>
> NOTE: My Hotmail account is not monitored regularly.
> To send me an e-mail, please use the address shown above.
>
> --
> View this message in context:
> http://spssx-discussion.1045642.n5.nabble.com/Comparing-two-Sobel-s-Z-tp5714957p5714958.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
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--
Alexander J. Shackman, Ph.D.
HealthEmotions Research Institute | Lane Neuroimaging Laboratory
Wisconsin Psychiatric Institute & Clinics
University of Wisconsin-Madison
6001 Research Park Boulevard
Madison, Wisconsin 53719

Telephone: [phone]
Fax: [phone]
Email: [hidden email]
http://psyphz.psych.wisc.edu/~shackman

[NomiW]

Bruce - thanks for your reply. It was very helpful.
One followup question: is there any reference I can cite when using this method in a manuscript?
Thanks,
Nomi

[Bruce Weaver]

Hi Nomi.  You should be able to find this in any of a number of intermediate to advanced level stats texts.  E.g., here are two that I've just pulled off my shelf:

Howell, D.C. (2007). Statistical Methods for Psychology (6th Ed.).  -- see "variance sum law" on p. 193

Glass, G.V. & Hopkins, K.D. (1996). Statistical Methods in Education and Psychology (3rd Ed.).  -- see "The Variance of a Difference" on p. 129.  G&H show the general formula where Var(Diff12) = Var1 + Var2 - 2*COV12.  But when you have two independent samples, COV12 = 0.

HTH.

NomiW wrote

Bruce - thanks for your reply. It was very helpful.
One followup question: is there any reference I can cite when using this method in a manuscript?
Thanks,
Nomi

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