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# RE: st: Comparing coefficients across sub-samples

 From "Fitzgerald, James" To Lisa Marie Yarnell , "statalist@hsphsun2.harvard.edu" Subject RE: st: Comparing coefficients across sub-samples Date Thu, 2 Aug 2012 23:42:44 +0000

```Lisa,
Do I need to divide the squared standard errors by n of each sample?
The formula you provided appears to be Welch's t-test formula, but Welch's formula would be:
z = (B1 - B2) / √(seB1^2/n1 + seB2^2/n2)
Welch, B. L. (1947). "The generalization of "Student's" problem when several different population variances are involved". Biometrika 34 (1–2): 28–35
Regards
James

________________________________________
From: Lisa Marie Yarnell [lisayarnell@yahoo.com]
Sent: 01 August 2012 04:29
To: statalist@hsphsun2.harvard.edu; Fitzgerald, James
Subject: Re: st: Comparing coefficients across sub-samples

Hi James,

Typically the effect of a predictor in two different groups can be compared with the unstandardized beta. You can do a statistical test of the difference in the betas using the z-score formula below.  I usually just calculate the difference between unstandardized betas from two different models by hand, though Stata might have a command to do this for you.  Is that what you are looking for: the Stata command?

(b1 – b2)                       b1 and b2 are the unstandardized regression weights that you want
z = --------------------                                    to test the difference between
√(seb12 + seb22)                   seb1 and seb2are the standard errors of these unstandardized
↑                                                    regression weights, found next to the weights themselves
This is a square root sign!                      in your SPSS output.  Remember to square them.
Take the square root of the
entire value in parentheses.

In terms of comparing the *magnitude* of the effect in the two different subsamples, it is more correct to do this qualitatively by comparing the *standardized* beta for the variable of interest against effect size rules of thumb for small/medium/large (which sometimes differ by discipline, such as social sciences/education/engineering).  Just report the standardized beta as the effect size in each group; it would be a qualitative statement about the effect in each group.

Here are rules that I have:
Standardized regression coefficients:
* Keith’s (2006) rules for effects on school learning: .05 = too small to be considered meaningful, .above .05 = small but meaningful effect, .10 = moderate effect, .25 = large effect.
* Cohen’s (1988) rules of thumb: .10 = small, .30 = medium, >  (or equal to) .50 = large

Lisa

----- Original Message -----
From: "Fitzgerald, James" <J.Fitzgerald2@ucc.ie>
To: "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Cc:
Sent: Tuesday, July 31, 2012 4:14 PM
Subject: st: Comparing coefficients across sub-samples

Hi Statalisters

I am running the same model on two sub-samples as follows:

xtreg ltdbv lnta tang itang prof mtb if nolowlntalowtang==1, fe cluster(firm)

xtreg ltdbv lnta tang itang prof mtb if nolowlntalowtang==0, fe cluster(firm)

I want to compare the explanatory power of lnta across the two sub-samples i.e. in which sub-sample does lnta explain significantly more of the variation in ltdbv?

Can anyone give me some advice on how to achieve this?

James
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