ANCOVA Flashcards
what dos ANCOVA stand for?
analysis of covariance
what is the broad idea?
to analyse between group differences invariance (such as with ANOVA) - but after the effect from the variance from a covariate has been estimated and removed from the DV.
In this way, the DV variance gets smaller, and the comparison between the (theoretically untouched) IVs is comparatively larger, creating more power/effect.
what was the take home message from the lecture?
These techniques are often wrongly used in research with nonrandom assignment to groups.
What happens with non-random assignment of groups?
Variance is not random and overlapping variance between the covariant factor and factor of interest compromises the stats and becomes meaningless.
what are the three main purposes of ANCOVA?
1) To increase power by reducing error term in experimental work
2) To adjust for mismatch on some nuisance variable in non-experimental
3) follow up to MANOVA (not covered step-down analysis)
what is the issue with adjusting for mismatch on some nuisance variable?
Comparing across groups by shifting group means in line with another ‘nuisance’ variable mean held constant
Removal of variance from a covariate that is inextricably bound with the independent variable of interest would render the results of ANCOVA meaningless.
E.g LORDS PARADOX = comparing boys and girls for weight change over the course of a year. The boys weigh more than the girls at the start and end, and neither groups average weight changes over time. Did diet affect boys n girls differently throughout the year? by estimating and removing the effect of weight from the beginning of the year (covariate), one is adjusting all samples to the same mean weight (heavy boys regress toward the mean + light girls move toward to heavier mean) - so the ANCOVA analysis is meaningless, as OF COURSE boys get heavier as a function of weight, as they, in reality, were heavier at beginning and end.
ANCOVA is equivalent to …
multiple regression (with categorical predictors)
A potential covariate is any variable that is significantly
correlated with the outcome variable, DV (if not it’s just noise = no relation – so you start to put things in that you know etc, bit of swindling)
We assume a xxx relationship between the covariate (x) and the DV (y)
linear r (it’s a general linear model GLM
ANCOVA removes the xxxx variation, explained by the xxxxx
ANCOVA removes the portion of the DV variation, explained by the covariate
ANCOVA thus increases xxxx xxxx to assess the effects of the group factor(s).
and thus increases statistical power to assess the effects of the group factor(s).
The MEAN is adjusted by using …
regression slopes
Ð We make a slope toward the DV for every IV.
Ð We then slide the mean up-or-down for each IV group toward the set mean of the covariate
Ð In this way, all are compared at a set point
technical
ANCOVA uses the regression line between IVs on each subject and calculating each predicted score on the DV based on just the covariate, as if they had scored at the mean of ALL participants on the covariate. Everyone’s score on the DV is adjusted AS IF they all scored at the mean on the covariate.
ANCOVA addresses the same questions about IVs that ANOVA does ……
main and interaction effects, specific comparisons and contrasts
The effects of IVs are assessed holding covariates …
constant (i.e., treating each subject as if they scored at the overall mean for the covariate)
what are the usual ANOVA ASSUMPTIONS
Absence of outliers
Homogeneity of variance
