C532: ANOVA & Regression Modeling
Nov 9, 2011
Y. Cao
1
Topics:
learn about
ANCOVA model
.and realize it with the general linear model
procedure in SPSS.
Datasets
: C530_clbp.sav
References: lecture note and PCCR books on statistics.
In general, we can say that ANCOVA, an abbreviation of
analysis of covariance,
is a
combination of 2 types of ANOVA.
In common situation, we say that the ANOVA
model is
where X1 represents a nominal categorical variable, for example, treatment group; in
the other case,
X1 can be a continuous type of variable like Age, or RMQ. Both are
simple linear regressions.
In the first case, so called one way ANOVA model, we have one nominal categorical
variable (a fixed factor) to explain the outcome. A fixed factor, we say so because the
levels of the factor, like treatment groups 1, 2, 3 and 4 (or A, B, C, D or whatever name
you like), once assigned (usually randomly) to a patient, they are
fixed/constant
.
Now, we want to include one more variable to predict the outcome, this comes out a
continuous variable, called
covariate
, to explain more variations in the outcome.
Covariate means the continuous variable
vary together
with the fixed factor to affect
the outcome. After considering this supplementary
covariate, we then want to adjust
the group means (in SPSS, it is called
Estimated Marginal Means
), meaning usually we
would like to change it a little bit on the original group means. Then, ANCOVA is born.
It is a multiple linear regression.
Correspondingly, the ANOVA table for ANCOVA is a combination of the 2 ANOVA
tables. See the lecture notes, the 3 tables on page 1.
ANCOVA is to test/
compare
mean differences between factor levels (in our case,
treatment groups) and
adjusted for
the effect of the covariate(s).
ANCOVA will
generally
increase our power to detect true meaningful group mean
differences because the inclusion of the covariate will usually explain more variability in
the outcome variable (the Y).