why does F value reduce in ANCOVA if error is reduced?

#1
hey there,
a stressed undergrad here trying to get to grips with ANCOVA. One of the advantages of ANCOVA versus ANOVA is that it reduces the error term and thus increases power. If you do a regular ANOVA, you get the F value. If you then include a covariate and perform ANCOVA - this F value is reduced. How is it reduced (especially if the error term is being reduced)? I guess I don't understand the stats workings behind ANCOVA and what its doing to eliminate the covariate.
Any help would be greatly appreciated as I have an exam next week:p

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Just noticed that the example I'm using in spss is where the means of the covariate are different for 3 levels of the IV. when I change this in spss so that the means of the CV are the same for all IV levels, the F value increases (compared to regular ANOVA). But I still don't get what calculations spss is doing to remove the CV and how differences in the CV mean affect this?? My text book doesn't cover ANCOVA, my lecturers notes don't go into this detail and I just can't understand explanations of ANCOVA from the net:-/
help?

cheers,

Karen
 
Last edited:

Karen

New Member
#2
answered my own question

after battling for days, i've finally figured out what's what with ANCOVA.
in short if the CV has different means for each level of the IV then they are somewhat correlated so ANCOVA adjusts the DV means (to rule out this correlated part) as if the CV means were all the same in each IV level/group (ie substitutes the different CV means in each group for the average CV mean - hence adjusting the DV). The greater the difference between the real CV means and the substituted CV mean the more the Mean Square value for the DV is reduced in addition to reducing the error term so the F value could be reduced.
On the flip side, if the CV mean is the same for all levels of the IV, there's no need to adjust the DV means for each IV level but it still reduces the error term and F is increased.

phew .....