Re: Statistical methods to investigate interactions between factors

[Jeffrey Berman]

On 12/14/06 1:48 PM, "Kersting, Nicole" <[hidden email]> wrote:

> Hi all,
> =20
> I ran an ANCOVA model which yielded a significant interaction between a
> fixed factor and a continuous covariate.  I am interested in
> investigating the interaction further but I ran into the following
> problem:  I created a median split in the continuous covariate, which in
> combination with the factor gave me four means for pairwise comparisons.
> While I realize all the issues attached to median splits, I have the
> additional problem that the pairwise comparisons weren;t significant,
> indicating that the interactions is not represented well by the median
> split.
> =20
> So I am wondering if there are any other statistical methods to
> investigate an interaction between a continuous covariate and a factor
> or if I am doomed to fish around for the appropriate split because for
> reporting purposes I will need the pairwise comparisons.  What do people
> do in general in those cases.  Given that we didn't expect the
> interaction (not part of the design) it's hard to come up with a
> theoretical rationale on how to split the data for pairwise comparisons
> and graphs.
> =20
> Many thanks in advance,
> Nicki

Nicki:

The alternative to splitting the continuous variable into categories is to
use the Johnson-Neyman technique, which identifies regions of significance
when there is an interaction between a categorical and continuous variable.
A discussion of this approach can be found in chapter 14 of the following
Pedhazur text:

Pedhazur, E. J. (1997). Multiple regression in behavioral research:
Explanation and Prediction (3rd ed.). Fort Worth, TX: Harcourt Brace.

Implementing this procedure in SPSS is described in the following:

Karpman, M. B. (1983). The Johnson-Neyman technique using SPSS or BMDP.
Educational and Psychological Measurement, 43, 137- 147.

Karpman, M. B. (1986). Comparing two non-parallel regression lines with the
parametric alternative to analysis of covariance using SPSS-X or SAS: The
Johnson-Neyman technique. Educational and Psychological Measurement, 46,
639-644.

Pedhazur provides a revised version of the SPSS code from one of the Karpman
articles.

Example code is also described in an answer in the SPSS Knowledgebase.  If
you are registered with SPSS technical support, you can access this answer
by searching for Resolution #19193 in the SPSS Knowledgebase. And here is
the direct link to this answer:

http://tinyurl.com/yzc6yz

Be aware that the examples in the above material are for situations
involving a two-level categorical variable and it appears your categorical
factor has more than two levels.  Pedhazur provides some references for
extending the Johnson-Neyman technique in these cases.  Perhaps the simplest
explanation for using the Johnson-Neyman technique in the multiple-group
situation can be found in chapter 13 of the following out-of-print text by
Huitema:

Huitema, B. E. (1980). Analysis of covariance and alternatives. New York:
Wiley.

Good luck with your analyses.

-Jeffrey Berman