On Mon, 3 Jul 2000, Miguel Verdu wrote:
> In an ANCOVA where covariate interacts with the independent variable,
> should the covariate be nested within the independent variable?. I
> would appreciate bibliographic references on this matter.
In general, interaction can be observed only if the interacting variables
are crossed. If they are nested, "interaction" is not defined.
Thus for a one-factor ANCOVA the conventional sources of variation are
the factor (A, say), the covariate (X), and their interaction (A*X).
(The existence of a significant interaction implies that the slope of the
dependent variable Y on X is not constant across the several levels of
A.)
A good basic treatment of ANCOVA, explicitly including interaction
between factor(s) and covariate(s), can be found in Tatsuoka's book on
multivariate analysis. Chapter 3, as I recall.
Some standard statistical-package ANCOVA routines do not permit such a
model to be analyzed; in which case you will wish to use either a
general-linear-model (GLM) routine or a multiple-regression routine,
either of which will permit more elaborate models, as well as
unconventional models, to be analyzed.
For an example of a three-factor ANCOVA in which all the
interactions were modeled in a multiple regression analysis, see a
White Paper of mine on the Minitab web site:
http://www.minitab.com
(Whether the conventional sources of variation provide the most useful
way of reporting your results is another question entirely, answers to
which tend to depend at least in part on the pattern of results.)
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
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