I just noticed that the Gregory Chow citation below was missing the year.
The full citation is:
Chow, G.C. (1960). Tests of equality between sets of coefficients in two
linear regressions, Econometrica, 28(3), 591-605.
I'll also take this opportunity to stress that this approach is testing the
equality of slopes AND intercepts across groups. The coefficient for the
dummy variable for group is the estimated increase in the intercept for the
group coded 1.
SPSS Technical Support
From: Matheson, David
Sent: Thursday, November 09, 2000 11:38 AM
Subject: Re: comparing b's or beta's
The Chow test provides a test of the equality of a set of coefficients
across groups. You set up a dummy variable for gender and interaction
variables involving gender and the other predictors. Here is a technical
note on running Chow's test in SPSS. It is available as solution 100000298
on the AnswerNet at http://www.spss.com/tech/answer/index.cfm .
I've actually modified the text slightly below. When the solution was
written, the change in R^2 could not be requested in the menus. That
statistic is now available in the Statistics dialog of the Regression
procedure, as of SPSS 7.5. If you're running an earlier version of SPSS than
that, you'll need to run the procedure as a syntax command. You can build
most of the command in the dialog boxes, paste it to a syntax window and add
the keyword CHA to the /STATISTICS subcommand.
The example in the solution uses only 1 predictor (other than those
computed for the purpose of the Chow) test, but the approach is
generalizable to multiple predictors. You would then have the 1 dummy
variable for sex and a sex*predictor interaction term for each of the
predictors in the original model. The unstandardized coefficient for the
edlevel*sex interaction in this example is the estimated increase in the
slope for edlevel for those cases where sex = 1.
SPSS Technical Support
Chow test for equal sets of regression coefficients across groups
What is the formula for the Chow test for equal regression
parameters across groups? Will SPSS perform this test?
There is no SPSS procedure or keyword which requests the Chow test
by name, but the test is easy to obtain from the REGRESSION procedure.
The Chow test provides a test of whether the set of linear regression
parameters, i.e. the intercepts and slopes, is equal across groups.
For example, suppose we use the variable SALNOW from SPSS for
Windows' bank.sav sample data set as our dependent variable and
EDLEVEL as our predictor. Also suppose that we want to know whether
the intercept and slope for this regression are equal for men and women.
The algorithm for the Chow test is as follows:
1. Run the regression on men and women together and note the
residual sum of squares and degrees of freedom. Call this
RSS1 and DF1.
2. Run the regression separately for men and women and total
the residual sums of squares and degrees of freedom from the
two regressions. Call these RSS2 and DF2.
3. Find (RSS1 - RSS2)/(DF1 - DF2) .
4. Divide the result of step3 by RSS2/DF2 and compare this result to
the F distribution with (DF1-DF2) and DF2 degrees of freedom.
The null hypothesis for this test is that the regression intercept
and slope are both independent of gender.
You can perform this test in SPSS REGRESSION and also obtain separate
tests for the equality of intercept and slope across genders. The group
variable should be a dummy variable which equals 0 for 1 group; 1 for
the other. The bank.sav variable SEX is already in this form, with a
value of 1 representing female. An interaction term is computed as the
product of the predictor of interest (EDLEVEL) and SEX. REGRESSION is
run first with only EDLEVEL as a predictor. SEX and the interaction
term, called EDSEX in this example, are then entered in a second step
with a second /METHOD = ENTER subcommand. The change in R square is
requested with the keyword CHA in the /STATISTICS subcommand. This
keyword also requests a test of whether the change in R square is
greater than 0. This test is equivalent to the CHOW test as calculated
from steps 1 to 4 above. The standard statistical output from
REGRESSION also provides tests and confidence intervals for the SEX
and EDSEX coefficients, which are effectively adjustments to the
intercept and slope parameters, respectively, for female respondents.
The REGRESSION command to perform this analysis is presented below.
COMPUTE edsex = edlevel * sex .
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/STATISTICS COEFF OUTS CI R ANOVA END CHA
/METHOD=ENTER sex edsex .
If there were K groups whose regression coefficients were to be
compared, you would compute K-1 dummy variables and multiply each of
these by the independent variable(s) to produce K-1 (sets of)
The Chow Test is introduced in Gregory Chow's paper, 'Tests of Equality
Between Sets of Coefficients in Two Linear Regressions', Econometrica,
For discussions of the dummy variable approach to the Chow test, see a
pair of papers by Damodar Gujarati in The American Statistician,
1970, 24(1), 50-52; and 1970, 24(5), 18-22.
From: William B. Ware [mailto:wbware@EMAIL.UNC.EDU]
Sent: Thursday, November 09, 2000 10:53 AM
Subject: Re: comparing b's or beta's
Would it be appropriate to "dummy" the gender variable and include it
along with its interactions... the tests on the interactions would be
tests for the equality of the regression coefficients, would they not?
William B. Ware, Professor and Chair Educational Psychology,
CB# 3500 Measurement, and Evaluation
University of North Carolina PHONE (919)-962-7848
Chapel Hill, NC 27599-3500 FAX: (919)-962-1533
http://www.unc.edu/~wbware/ EMAIL: firstname.lastname@example.org
On Thu, 9 Nov 2000, Dale Glaser wrote:
> Wim.......in the past I have used the formula from Cohen and Cohen (1983)
> page 56 when comparing the significance of the difference between
> independent Betas....Zar (1999) in chapter 18 (p. 360) in his
> Biostatistical Analysis text also has a section on comparing two slopes;
> however, and unfortunately I did not save it, I know some one developed a
> macro for the test of two independent betas..............hope this
> helps..........dale glaser
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of
> Sent: Wednesday, November 08, 2000 11:22 PM
> To: SPSSX-L@LISTSERV.UGA.EDU
> Subject: comparing b's or beta's
> Dear all,
> After having applied a hierarchical regression procedure in two
> groups separately (boys and girls) I want to compare the estimated
> parameters between the two groups, e.g. the b's (regression weights) or
> beta's (standardized). Is there any way to do it, either with computer
> power, either by hand (e.g. a kind of z-test like we have for comparing
> correlations) ?
> Someone with experience in this matter ?
> Wim Beyers