This preview shows pages 1–3. Sign up to view the full content.
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).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentC532: ANOVA & Regression Modeling
Nov 15, 2010
Y. Cao
2
However, adding covariate(s) will reduce the degrees of freedom, so, if the added
covariates only accounts for little variability in the outcome variable, then it
might
actually
decrease the statistical power.
In a simple ANCOVA modeling, in order to predict the outcome variable Y, we use 2
explanatory variables: one is a nominal categorical variable X
1
as the fixed factor
(because the levels of it are fixed) and one continuous variable X
2
(
covariate
).
Therefore, the model equation looks like:
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '11
 Long

Click to edit the document details