Both are correct.
If age is related to outcome, test score, and a predictor (in your case the factor sex) then one would include age in the model as age is a potential confounder of the relation between sex and test score. To be a confounder a variable must be related both to the outcome being studied (test score in your example) and to one or more predictor variables (sex in your example). A potential confounder is a real confounder if including the confounder in the model changes the relation between outcome and the predictor to which the confounder was related.
On the other hand if age is related to the outcome, e.g. as age increases so does test score, then one would want to include age in the model as age decreases the residual error of the model. Another way to say this is by including age we are improving our prediction of the outcome, test score. By decreasing the residual confounding including age would improve the over all F statistic and the model's R squared.
John
John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
>>> K F Pearce <[log in to unmask]> 10/26/2009 11:08 AM >>>
Hello everyone,
This is just a small question regarding the reasons why we use ANCOVA as the texts that I have read seem to differ in their explanations.
Say our dependent variable was 'test score' and our factor was 'gender'. We want to see if test score differs between genders.
(A) Now some (i.e. most!) texts say that if we found that age differs from person to person in our study (regardless of gender) then, because age is likely to be (linearly) related to test score, then we use ANCOVA with age as a covariate i.e. we are saying that, in effect, males and females have the same age range in our study.
(B) Another text (Brunig and Kintz, 1987 "Computational Handbook of Statistics")) uses an example for ANCOVA along the following lines - age is still related to test score but the sample of males in the study are younger than the sample of females (this could occur e.g. if one of our groups was comprised of primary school males and the other group secondary school females).
I would say that the criteria from ANCOVA are those of (A) above as often texts specifically say that for ANCOVA "the covariate is not related to treatment [i.e. group/factor]"...but I just thought I'd ask a second opinion.
Many thanks everyone - it's appreciated.
Kindest Regards,
Kim
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