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Science Forum Index » Statistics - Education Forum » Why ANCOVA?
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| Jean K |
 Posted: Fri Feb 22, 2008 12:01 am |
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Hi Group,
I need to repeat an analysis that was conducted on a smaller dataset,
but after looking at the previous statistician's methods, I'm a little
confused at why she chose to use ANCOVA. Any insight would be
appreciated!
Response Variable: Scores on 36 different Tests
Main Predictor of Interest is Treatment Type (1 or 2)
Data was collected from different individuals in each treatment group.
What she did:
1. Chi-square tests between Treatment Type and Clinical/Demographic
Factors (i.e. Race, Sex, Age) and identified 3 significant variables.
2. ANCOVA analyses for each continuous test score (36 separate
ANCOVAs) to identify significant differences between patients in
Treatment 1 vs. Treatment 2, while controlling for 3 categorical
demographic variables.
I don't have that much experience in ANCOVA, but I thought this is
used to control for continuous "covariates", or does it apply to
categorical ones too? Would a multiple linear regression in this case
be enough to control for the significant categorical variables
identified by the chi-square analyses?
Thanks very much,
Jean |
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| Richard Ulrich |
| Posted: Sat Feb 23, 2008 1:14 am |
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On Fri, 22 Feb 2008 02:01:35 -0800 (PST), Jean K <cjkuo584@gmail.com>
wrote:
Quote: Hi Group,
I need to repeat an analysis that was conducted on a smaller dataset,
but after looking at the previous statistician's methods, I'm a little
confused at why she chose to use ANCOVA. Any insight would be
appreciated!
Response Variable: Scores on 36 different Tests
Main Predictor of Interest is Treatment Type (1 or 2)
Data was collected from different individuals in each treatment group.
What she did:
1. Chi-square tests between Treatment Type and Clinical/Demographic
Factors (i.e. Race, Sex, Age) and identified 3 significant variables.
If Age was measured as continuous, then collapsing
it into categories for doing contingency tests is a waste
of power.
Quote:
2. ANCOVA analyses for each continuous test score (36 separate
ANCOVAs) to identify significant differences between patients in
Treatment 1 vs. Treatment 2, while controlling for 3 categorical
demographic variables.
I don't have that much experience in ANCOVA, but I thought this is
used to control for continuous "covariates", or does it apply to
categorical ones too? Would a multiple linear regression in this case
be enough to control for the significant categorical variables
identified by the chi-square analyses?
ANOVA can be regarded as a specific arrangement of
terms and tests which can all be obtained from OLS
regression. ANOVA "factors" with more than two levels
need to be coded into k-1 dummy variables, for k levels,
and "ANOVA" computer programs typically do all that for
you. To use a REGRESSION package, you might have
to construct the dummies as new variables to use
regression for more than two levels of categories.
ANCOVA is ANOVA whose overt layout has an increased
resemblance to regression. You do not get "counts" or
means for the subsidiary statistics for the covariates, which
would be available if those variables were included as factors.
The design you describe will give exactly the same result
as the regression, or as the ANOVA with 4 factors that
does not look at any interaction terms -- assuming that
the analyses are done correctly and elect similar options.
--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html |
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| Guest |
| Posted: Wed Mar 05, 2008 8:01 am |
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Quote: 2. ANCOVA analyses for each continuous test score (36 separate
ANCOVAs) to identify significant differences between patients in
Treatment 1 vs. Treatment 2, while controlling for 3 categorical
demographic variables.
I don't have that much experience in ANCOVA, but I thought this is
used to control for continuous "covariates", or does it apply to
categorical ones too? Would a multiple linear regression in this case
be enough to control for the significant categorical variables
identified by the chi-square analyses?
Your experiments did not "control" the effects of race, gender, and
age. In other words, your experiments did not assign samples
"randomly". For example, the people in the first treatment group are
much older than the people in the second group, the outcomes of your
experiments will be affected by "age". If you just do a t-test
(without knowing the age difference in the treatment groups), you may
conclude that there are treatment effects between the two groups. Are
they? Another example is the females in the first group exercise
regularly and eat vegetables a lot (but you did not know) while the
males in the second group are overweight (but you did not know), you
may conclude that there are gender differences.
Ahh, the endless questions of "Did you control this or that?" in
"OBSERVATIONAL" studies.
The KILLER in OBSERVATIONAL studies in understanding the cause-and-
effect relationship is the "collinearity" as the number of covariates
get larger. If two covariates are highly correlated, you can NOT
seperate the effects of the two covariates as well as the treatment
effects.
Hope this helps.
Sangdon Lee, Ph.D.,
GM Tech. Center. |
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