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From |
"Fitzgerald, James" <J.Fitzgerald2@ucc.ie> |

To |
"<statalist@hsphsun2.harvard.edu>" <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: Comparing coefficients across sub-samples |

Date |
Fri, 3 Aug 2012 01:33:45 +0000 |

Thanks David. That's a huge help. All the best James On 3 Aug 2012, at 02:26, "David Hoaglin" <dchoaglin@gmail.com> wrote: > James, > > The formula that Lisa gave is not Welch's t-test formula. Welch's > formula produces a t-test on the difference between the two underlying > means, and the expression inside the square-root sign is (s1^2)/n1 + > (s2^2)/n2, where s1^2 and s2^2 are the respective sample variances. > (Those sample variances are also used in calculating the number of > degrees of freedom for the t-test, which will generally not be an > integer.) > > In "Lisa's formula" the denominator is the square root of [se(B1)]^2 + > [se(B2)]^2, which can be written var(b1) + var(b2). It uses the fact > that, since B1 and B2 come from different groups (and can be assumed > to be independent), var(B1 - B2) = var(B1) + var(B2). Lisa is > replacing the true variances by their estimates from the two > regressions (the squares of the respective standard errors) and > referring z to the standard normal distribution. The standard errors > of B1 and B2 already incorporate n1 and n2, along with other features > of the regression data. > > David Hoaglin > > On Thu, Aug 2, 2012 at 7:42 PM, Fitzgerald, James <J.Fitzgerald2@ucc.ie> wrote: >> 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 > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: Comparing coefficients across sub-samples***From:*"Fitzgerald, James" <J.Fitzgerald2@ucc.ie>

**Re: st: Comparing coefficients across sub-samples***From:*David Hoaglin <dchoaglin@gmail.com>

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