alpha inflation when comparing regression coefficients?

[Marnie LaNoue]

Hi All --
Any comments appreciated. I tested a regression model with a categorical
variable to test for differences across groups. The interaction was
significant, so I ran the separate models for the groups and now want to
compare the significance of the difference of the betas using t-tests.
THere are two continuous predictors. Do I need to use an alpha adjustment?
And, do I need to do it 2 times for the difference in the 2 predictors
across the 2 groups? Is there an omnibus test that will get me the answer I
desire?
Thanks!
Marnie LaNoue, Ph.D.
University of New Mexico

[statisticsdoc]

Stephen Brand
www.statisticsdoc.com

Marnie,

Since the interaction was significant, you need not employ an alpha adjustment when you carry out the regressions separately by group.

BTW, it is entirely possible that when you carry out the regressions separately by group, the regression weights will not be significantly different from zero (say if the weight is slightly positive in one group and slightly negative in another group).  The interaction test indicates that these weights are significantly different from one another, and this is still the case even if the weights are not significantly different from zero when you carry out regressions by group.

HTH,

Stephen Brand


---- Marnie LaNoue <[hidden email]> wrote:

> Hi All --
> Any comments appreciated. I tested a regression model with a categorical
> variable to test for differences across groups. The interaction was
> significant, so I ran the separate models for the groups and now want to
> compare the significance of the difference of the betas using t-tests.
> THere are two continuous predictors. Do I need to use an alpha adjustment?
> And, do I need to do it 2 times for the difference in the 2 predictors
> across the 2 groups? Is there an omnibus test that will get me the answer I
> desire?
> Thanks!
> Marnie LaNoue, Ph.D.
> University of New Mexico

--
For personalized and experienced consulting in statistics and research design, visit www.statisticsdoc.com

[Richard Ristow]

At 10:20 AM 6/27/2006, Marnie LaNoue wrote:

>I tested a regression model with a categorical variable to test for
>differences across groups. The interaction was significant, so I ran
>the separate models for the groups and now want to compare the
>significance of the difference of the betas using t-tests.

If I understand correctly what you want, there's a simple technique
that's very useful.

If your dependent variable is Y, your two continuous predictors are A
and B, and G2 is an indicator variable for the second group, you can
formulate your model as

Y = a*A + b*B + a2*A*G2 + b2*B*G2 + G2 + constant + <epsilon>.

Then a2 is the difference of a for group 1, and 1 for group 2; etc.
That gives you a direct t-test for whether the coefficients are
significantly different.

You can also do an F-test against the hypothesis that a2 and b2 are
both 0, for testing whether there's any detectable difference in slopes
between the groups.

If you estimate the model this way, then the estimated a is the
coefficient of A for group 1, and (a+a2) is the coefficient for group
2; same for B.