It is a matter of emphasis. Both regression and
ANOVA are techniques for dealing with linear
models. ANOVA focuses on experiments where the
variables may be random and where there may be
several error terms. Regression on models which
tend to have fixed, continuous, independent fixed
variables and a single error term. To say that
ANOVA is a special case of regression, in effect
redefines regression as "linear model analysis,"
which can be done, but is a stretch. As definitive
a statement as is likely to be find is given by
Scheffé in The analysis of variance (1959), and a
good discussion of using multiple regression to
perform some ANOVA calculations for fixed effect
models is given in Draper and Smith's Applied
regression analysis (1966).
I speculate that this now seems confusing because
texts in applied areas have perhaps dwelt too
heavily on the mechanics of ANOVA calculations and
mentioned the linear model part only briefly. The
upshot is that students in those areas are
surprised when the linear model part is called to
their attention, and apparently Jacob Cohen (1968)
felt strongly enough about it to write a paper
explaining the connection. Standard statistical
texts have always insisted on the mathematics, and
Kempthorne for example in Design and analysis of
experiments (1952) takes great pains to structure
ANOVA in terms of linear models -- he even derives
the normal equations.
Alexander Tsyplakov wrote:
>
> An interesting problem have arised during discussion of the
> origins of "eigenvalue".
>
> My own point of view is that ANOVA is just a particular case
> of regression analysis with dummy (1/0) regressors and
> either fixed or random effects. Block orthogonality of
> regression matrix in the special case of ANOVA makes it
> possible to decompose the sum of squared residuals (and
> variance) into several components.
>
> If people misuse the term ANOVA then what is it's correct
> meaning? Is it a statistical model which is different from
> regression model y=Xb+e? Then there must be some clear
> formal discription.
>
> -----------------------------
> Alexander Tsyplakov
> Novosibirsk State University
> http://www.nsu.ru/ef/tsy/
>
> Elliot Cramer wrote...
> > Werner Wittmann <[EMAIL PROTECTED]>
> wrote:
> > : inverting the
> > : correlation matrix to get the effects was too
> complicated to compute by
> > : hand, so Sir Ronald developed the ANOVA shortcut.
> >
> > hardly. They do have some mathematics in common (through
> use of dummy
> > variables which some of us think is for dummies). they
> are comceptually
> > completely different/ Unfortunately many people misuse
> ANOVA because they
> > think of it as regression analysis.
>
> > : I'm always teasing my colleagues and students, if you
> spent one year
> > : learning ANOVA and one year multiple regression you've
> wasted almost one
> > : year of your life.
>
> > you can learn the mathematics of regression analysis in 10
> minutes but
> > you're still a long way from understanding either it or
> ANOVA
--
Bob Wheeler --- (Reply to: [EMAIL PROTECTED])
ECHIP, Inc.
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
